; The coefficients form a pattern called Pascals Triangle, where each number is the sum of the two numbers above it.

In the binomial expansion of (2 - 5x) 20, find an expression for the coefficient of A Bionomial Expansion is a linear polynomial raised to a power, like this (a + b) n.As n increases, a pattern emerges in the coefficients of each term. TI-85 rom code download, solving binomial equations, printable math money for 1st grade, algebraic expressions poem, modern biology skills worksheet answers. Binomial Theorem Calculator Cosine Calculator. Practice your math skills and learn step by step with our math solver. The binomial theorem is very helpful in algebra and in addition, to calculate permutations, combinations and probabilities. It normally comes

Binomial Expression: A binomial expression is an algebraic expression that contains two dissimilar terms. Expanding binomials.

The formula used by the Maclaurin series calculator for computing a series expansion for any function is: Where f^n(0) is the nth order derivative of function f(x) as evaluated and n is the order x = 0. When the exponent is 1, we get the original value, unchanged: (a+b) 1 = a+b. ()!.For example, the fourth power of 1 + x is

This calculators lets you calculate expansion (also: series) of a binomial. So now we use a simple approach and calculate the value of each element of the series and print it .

Logarithmic expansion: expand_log. For values of x which are close to zero, we can ignore larger powers of n to approximate the power of a number. You can find the series expansion with a formula: Binomial Series vs. Binomial Expansion. When the exponent is 1, we get the original value, unchanged: (a+b) 1 = a+b. Pascal's triangle and binomial expansion. in the denominator of each term in the infinite sum. In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem.Commonly, a binomial coefficient is indexed by a pair of integers n k 0 and is written (). 3. It can be generalized to add multifaceted exponents for n. Having A binomial Theorem is a powerful tool of expansion, which has application in Algebra, probability, etc. We will use the simple binomial a+b, but it could be any binomial.

The binomial series is named because its a seriesthe sum of terms in a sequence (for example, 1 + 2 + 3) and its a binomial two quantities (from the Latin binomius, which means two names).

What is a Binomial Expansion Calculator? karen and ron i survived; is john bowman from sha na na still alive; most accurate single bet of the day Binomial series.

Sal expands (3y^2+6x^3)^5 using the binomial theorem and Pascal's triangle. This calculator will try to simplify a polynomial as much as possible. b is the second term of the binomial and its exponent is r 1, where r is the term number. Independent term of x in (x + y) n: First of all, think what does a term independent of x in Binomial Theorem mean? 1 See answer Advertisement Advertisement chaseashley24 is waiting for your help. Binomial Expansion Calculator Binomial Theorem Calculator Using Pascals Triangle. \left (x+3\right)^5 (x+3)5 using Newton's binomial theorem, which is a formula that allow us to find the expanded form of a binomial raised to a Process 1: Enter the complete equation/value in the input box i.e. It expands a polynomial expression and finds its sum. For example: ( a + 1) n = ( n 0) a n + ( n 1) + a n 1 + + ( n n) a n. We often say "n So, counting from 0 to 6, the Binomial Theorem gives me these seven terms: The coefficients occuring in the binomial theorem are known as binomial coefficients. The binomial expansion formula includes binomial coefficients which are of the form (nk) or (nCk) and it is measured by applying the formula (nCk) = n! In Algebra, binomial theorem defines the algebraic expansion of the term (x + y) n. It defines power in the form of ax b y c. The exponents b and c are non-negative distinct integers and b+c = n and the coefficient a of each term is a positive integer and the value depends on n and b. The sum of the powers of x and y in each term is equal to the power of the binomial i.e equal to n. The powers of x in the expansion of are in descending order while the powers of y are in ascending order. Find the value of q/p. Binomial coefficient is an integer that appears in the binomial expansion. This tutorial is developed in such a way that even a student with modest mathematics background can understand this particular topics in mathematics. 1+1.

n + 1. Featured on Meta Announcing the arrival of Valued Associate #1214: Dalmarus . Which can be simplified to: Where both n and k are integers. Find the first four terms in ascending powers of x of the binomial expansion of 1 ( 1 + 2 x) 2. The binomial series is the power series Step 1: In the input field, enter the required values or functions. It can be generalized to add multifaceted exponents for n. Having Here we look for a way to determine appropriate values of x using the binomial expansion. A binomial is an algebraic expression containing 2 terms. This leaves the terms (x 0) n in the numerator and n! 2. 1. Remember the laws of exponents? As the power increases the expansion of terms becomes very lengthy and tedious to calculate. So, the expansion is (a - b) 4 = a 4 - 4a 3 b + 6a 2 b 2- 4a b 3 + b 4. The 4th term in the 6th line of Pascals triangle is 10. The answer will ultimately depend on the calculator you are using. Expand using the Binomial Theorem (1-x)^3. Get the free "Binomial Expansion Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. to estimate the value of 2.03 10. So the 4th term is 10(2x)2( 3)3 = 1080x2 The 4th term is 21080x . The Pascal triangle calculator constructs the Pascal triangle by using the An online binomial theorem calculator helps you to find the expanding binomials for the given binomial equation. The binomial expansion calculator is an important tool in algebra and calculus. 1) A binomial coefficients C (n, k) can be defined as the coefficient of X^k in the expansion of (1 + X)^n.

the expansion calculator allows to expand online all forms of mathematical expressions, the expression can be alphanumeric, ie it can contain numbers and letters : Expand the following Binomial Theorem Expansion and the Binomial Coefficients . 1. Created by T. Madas Created by T. Madas Question 3 Find, without using a calculator, the binomial expansion of a) ( )7 2x 3 b) ( )5 2x+ 5 c) ( )3 2x 4 343 294 84 8x x x3 2 + , 3125 6250 5000 2000 400 32x x x x x5 4 3 2+ + + + + , 81 216 216 96 16x x x x4 3 2 + +

The binomial theorem is very helpful in algebra and in addition, to calculate permutations, combinations and probabilities.

We can expand the expression. Each expansion is a polynomial. a is the first term of the binomial and its exponent is n r + 1, where n is the exponent on the binomial and r is the term number. The taylor series calculator allows to calculate the Taylor expansion of a function. It can be easily calculated with the help of the Binomial Theorem. Show Solution.

This is also known as the binomial formula. k!) The Binomial Theorem is the method of expanding an expression that has been raised to any finite power.

(The calculator also reports the cumulative probabilities.

Search a Unit to Convert. Intro to the Binomial Theorem. That is, since (x + y)^6 = x^6 + 6x^5y + 15x^4y^2 + 20x^3y^3 + 15x^2y^4 + 6xy^5 + y^6, the program is meant to obtain the numbers 1, 6, 15, 20, 15, 6, 1 given only the input 6. Exponent of 1.

The equation for the binomial coefficient (n choose k or on a calculator) is given by: Now on to the binomial. In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yesno question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 p).A single success/failure Revista dedicada a la medicina Estetica Rejuvenecimiento y AntiEdad. Input the function you want to expand in T r+1 is the General Term in the binomial expansionThe General term expansion is used to find the terms mentioned in the above formula.To find the terms in the binomial expansion we need to expand the given expansion.Suppose (a + b) n is the equation then the series of its binomial expansion will be as follows:

across Provide

Follow the below steps to get output of Binomial Series Calculator.

If a = 1, no coefficient will be placed in front of the variable. Add your answer and earn points. State the range of validity for your expansion.

This binomial expansion calculator with steps will give you a clear show of how to compute the expression (a+b)^n (a+b)n for given numbers a a, b b and n n, where n n is an integer. [ ( n k)! Step 2: For output, To find the binomial coefficients for ( a + b) n, use the n th row and always start with the beginning. The first term is a n and the final term is b n. Progressing from the first term to the last, the exponent of a decreases by.

Enter the number of rows and hit the Calculate button for binomial expansion using Pascals triangle calculator. \displaystyle {n}+ {1} n+1 terms. n. Substitute the expression Follow the given process to use this tool. a) Find the first 4 terms in the expansion of (1 + x/4) 8, giving each term in its simplest form. b) Use your expansion to estimate the value of (1.025) 8, giving your answer to 4 decimal places. In the binomial expansion of (2 - 5x) 20, find an expression for the coefficient of x 5. Find the Taylor series expansion of any function around a point using this online calculator. So if you were expanding (ax + b) 5: The power is 5 and the term number is whichever term you are interested in.

CCSS.Math: HSA.APR.C.5. Binomial Coefficient Calculator. Given that the coefficient of x 3 is 3 times that of x 2 in the expansion (2+3x) n, find the value of n. Difficult question involving the use of nCr formula. The exponents of a start with n, the power of the binomial, and decrease to 0.

Integration By Parts Calculator: Want to calculate the integration by parts of an expression in an easy way?Then you must go through the below sections of this page.

Binomial. The first term in the binomial is "x 2", the second term in "3", and the power n for this expansion is 6.

Binomial Expansion Calculator The binomial theorem is used to expand the binomials expression to any given power without direct multiplication. For any binomial expansion of (a+b) n, the coefficients for each term in the expansion are given by the nth row of Pascals triangle. Term Independent of x in Binomial Theorem Algebra > Binomial Theorem > Independent Term of x 8.

Algebra1help.com contains helpful tips on binomial expansion calculator with steps, complex and rational expressions and other math subjects. Here, the coefficients n C r are called binomial coefficients.

For example, if a binomial is raised to the power of 3, then looking at the 3rd row of Pascals triangle, the coefficients are 1, 3, 3 and 1. Binomial Expansion.

1 - Enter and edit the expression to expand and click "Enter Expression" then check what you have entered.

A binomial distribution is the probability of something happening in an event.

Now on to the binomial. In this way, using pascal triangle to get expansion of a binomial with any exponent. Enter required values and click the Calculate button to get the result with expansion using binomial theorem calculator. * (r)!) Example 7 : Find the 4th term in the expansion of (2x 3)5. The binomial theorem inspires something called the binomial distribution, by which we can quickly calculate how likely we are to win $30 (or equivalently, the likelihood the coin comes up heads 3 times). This is a very simple tool for Binomial Expansion Calculator. As we have explained above, we can get the expansion of (a + b) 4 and then we have to take positive and negative signs alternatively staring with positive sign for the first term.

The binomial theorem.

Whenever you need help on inverse functions or Expand and simplify polynomials. 1. Exponent of 0.

The following are the properties of the expansion (a + b) n used in the binomial series calculator. In each term, the sum of the exponents is n, the power to which the binomial is raised. k!]. n C r = (n!) Binomial Expansion Calculator to the power of: EXPAND: Computing Get this widget.

The binomial expansion calculator is used to solve mathematical problems such as expansion, series, series extension, and so on. This operation is built in to Take any function to get the binomial expansion. Step 2: Now click the button Expand to get the expansion. "=COMBIN (n, k)" where

An online binomial theorem calculator helps you to find the expanding binomials for the given binomial equation. The binomial coefficients ${n\choose k}$ that the above calculator compute are included in the binomial expansion Use of Pascals triangle to solve Binomial ExpansionInitially, the powers of x start at n and decrease by 1 in each term until it reaches 0.After that, the powers of y start at 0 and increase by one until it reaches n.Then, the n row of Pascal's triangle will be the expanded series' coefficients when the terms are arranged.More items Another interesting use of the binomial expansion is to calculate estimations of powers. In the expansion of a binomial term (a + b) raised to the power of n, we can write the general and middle terms based on the value of n. Before getting into the general and middle terms in binomial expansion, let us recall some basic facts about binomial theorem and expansion.. The binomial expansion formula is given by (a+b) n = k=0 to n (n!/ (n-k)! Firstly, write the expression as ( 1 + 2 x) Binomial Theorem Calculator Get detailed solutions to your math problems with our Binomial Theorem step-by-step calculator. Algebra. x 0 = 1. The binomial theorem widely used in statistics is simply a formula as below : ( x + a) n. =.

(2) 1 2 x = 2 y 2 = y 2 2 = 1 y 1 2 x. Created by Sal Khan. SolveMyMath's Taylor Series Expansion Calculator. Found the clue? Know the definition, explanation, terms and solved examples on binomial theorem and expansion. binomial_expand uses zip (range (1, len (coefficients)+1), coefficients) to get pairings of the each coefficient and its one-based index.

Find more Mathematics widgets in Wolfram|Alpha.

If a = -1, a "-" will be placed in front of the variable. The binomial expansion calculator is used to solve mathematical problems such as expansion, series, series extension, and so on.

Binomial Theorem - Challenging question with power unknown.

In the binomial expansion of (2 - 5x) 20, find an expression for the coefficient of A Bionomial Expansion is a linear polynomial raised to a power, like this (a + b) n.As n increases, a pattern emerges in the coefficients of each term. TI-85 rom code download, solving binomial equations, printable math money for 1st grade, algebraic expressions poem, modern biology skills worksheet answers. Binomial Theorem Calculator Cosine Calculator. Practice your math skills and learn step by step with our math solver. The binomial theorem is very helpful in algebra and in addition, to calculate permutations, combinations and probabilities. It normally comes

Binomial Expression: A binomial expression is an algebraic expression that contains two dissimilar terms. Expanding binomials.

The formula used by the Maclaurin series calculator for computing a series expansion for any function is: Where f^n(0) is the nth order derivative of function f(x) as evaluated and n is the order x = 0. When the exponent is 1, we get the original value, unchanged: (a+b) 1 = a+b. ()!.For example, the fourth power of 1 + x is

This calculators lets you calculate expansion (also: series) of a binomial. So now we use a simple approach and calculate the value of each element of the series and print it .

Logarithmic expansion: expand_log. For values of x which are close to zero, we can ignore larger powers of n to approximate the power of a number. You can find the series expansion with a formula: Binomial Series vs. Binomial Expansion. When the exponent is 1, we get the original value, unchanged: (a+b) 1 = a+b. Pascal's triangle and binomial expansion. in the denominator of each term in the infinite sum. In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem.Commonly, a binomial coefficient is indexed by a pair of integers n k 0 and is written (). 3. It can be generalized to add multifaceted exponents for n. Having A binomial Theorem is a powerful tool of expansion, which has application in Algebra, probability, etc. We will use the simple binomial a+b, but it could be any binomial.

The binomial series is named because its a seriesthe sum of terms in a sequence (for example, 1 + 2 + 3) and its a binomial two quantities (from the Latin binomius, which means two names).

What is a Binomial Expansion Calculator? karen and ron i survived; is john bowman from sha na na still alive; most accurate single bet of the day Binomial series.

Sal expands (3y^2+6x^3)^5 using the binomial theorem and Pascal's triangle. This calculator will try to simplify a polynomial as much as possible. b is the second term of the binomial and its exponent is r 1, where r is the term number. Independent term of x in (x + y) n: First of all, think what does a term independent of x in Binomial Theorem mean? 1 See answer Advertisement Advertisement chaseashley24 is waiting for your help. Binomial Expansion Calculator Binomial Theorem Calculator Using Pascals Triangle. \left (x+3\right)^5 (x+3)5 using Newton's binomial theorem, which is a formula that allow us to find the expanded form of a binomial raised to a Process 1: Enter the complete equation/value in the input box i.e. It expands a polynomial expression and finds its sum. For example: ( a + 1) n = ( n 0) a n + ( n 1) + a n 1 + + ( n n) a n. We often say "n So, counting from 0 to 6, the Binomial Theorem gives me these seven terms: The coefficients occuring in the binomial theorem are known as binomial coefficients. The binomial expansion formula includes binomial coefficients which are of the form (nk) or (nCk) and it is measured by applying the formula (nCk) = n! In Algebra, binomial theorem defines the algebraic expansion of the term (x + y) n. It defines power in the form of ax b y c. The exponents b and c are non-negative distinct integers and b+c = n and the coefficient a of each term is a positive integer and the value depends on n and b. The sum of the powers of x and y in each term is equal to the power of the binomial i.e equal to n. The powers of x in the expansion of are in descending order while the powers of y are in ascending order. Find the value of q/p. Binomial coefficient is an integer that appears in the binomial expansion. This tutorial is developed in such a way that even a student with modest mathematics background can understand this particular topics in mathematics. 1+1.

n + 1. Featured on Meta Announcing the arrival of Valued Associate #1214: Dalmarus . Which can be simplified to: Where both n and k are integers. Find the first four terms in ascending powers of x of the binomial expansion of 1 ( 1 + 2 x) 2. The binomial series is the power series Step 1: In the input field, enter the required values or functions. It can be generalized to add multifaceted exponents for n. Having Here we look for a way to determine appropriate values of x using the binomial expansion. A binomial is an algebraic expression containing 2 terms. This leaves the terms (x 0) n in the numerator and n! 2. 1. Remember the laws of exponents? As the power increases the expansion of terms becomes very lengthy and tedious to calculate. So, the expansion is (a - b) 4 = a 4 - 4a 3 b + 6a 2 b 2- 4a b 3 + b 4. The 4th term in the 6th line of Pascals triangle is 10. The answer will ultimately depend on the calculator you are using. Expand using the Binomial Theorem (1-x)^3. Get the free "Binomial Expansion Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. to estimate the value of 2.03 10. So the 4th term is 10(2x)2( 3)3 = 1080x2 The 4th term is 21080x . The Pascal triangle calculator constructs the Pascal triangle by using the An online binomial theorem calculator helps you to find the expanding binomials for the given binomial equation. The binomial expansion calculator is an important tool in algebra and calculus. 1) A binomial coefficients C (n, k) can be defined as the coefficient of X^k in the expansion of (1 + X)^n.

the expansion calculator allows to expand online all forms of mathematical expressions, the expression can be alphanumeric, ie it can contain numbers and letters : Expand the following Binomial Theorem Expansion and the Binomial Coefficients . 1. Created by T. Madas Created by T. Madas Question 3 Find, without using a calculator, the binomial expansion of a) ( )7 2x 3 b) ( )5 2x+ 5 c) ( )3 2x 4 343 294 84 8x x x3 2 + , 3125 6250 5000 2000 400 32x x x x x5 4 3 2+ + + + + , 81 216 216 96 16x x x x4 3 2 + +

The binomial theorem is very helpful in algebra and in addition, to calculate permutations, combinations and probabilities.

We can expand the expression. Each expansion is a polynomial. a is the first term of the binomial and its exponent is n r + 1, where n is the exponent on the binomial and r is the term number. The taylor series calculator allows to calculate the Taylor expansion of a function. It can be easily calculated with the help of the Binomial Theorem. Show Solution.

This is also known as the binomial formula. k!) The Binomial Theorem is the method of expanding an expression that has been raised to any finite power.

(The calculator also reports the cumulative probabilities.

Search a Unit to Convert. Intro to the Binomial Theorem. That is, since (x + y)^6 = x^6 + 6x^5y + 15x^4y^2 + 20x^3y^3 + 15x^2y^4 + 6xy^5 + y^6, the program is meant to obtain the numbers 1, 6, 15, 20, 15, 6, 1 given only the input 6. Exponent of 1.

The equation for the binomial coefficient (n choose k or on a calculator) is given by: Now on to the binomial. In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yesno question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 p).A single success/failure Revista dedicada a la medicina Estetica Rejuvenecimiento y AntiEdad. Input the function you want to expand in T r+1 is the General Term in the binomial expansionThe General term expansion is used to find the terms mentioned in the above formula.To find the terms in the binomial expansion we need to expand the given expansion.Suppose (a + b) n is the equation then the series of its binomial expansion will be as follows:

across Provide

Follow the below steps to get output of Binomial Series Calculator.

If a = 1, no coefficient will be placed in front of the variable. Add your answer and earn points. State the range of validity for your expansion.

This binomial expansion calculator with steps will give you a clear show of how to compute the expression (a+b)^n (a+b)n for given numbers a a, b b and n n, where n n is an integer. [ ( n k)! Step 2: For output, To find the binomial coefficients for ( a + b) n, use the n th row and always start with the beginning. The first term is a n and the final term is b n. Progressing from the first term to the last, the exponent of a decreases by.

Enter the number of rows and hit the Calculate button for binomial expansion using Pascals triangle calculator. \displaystyle {n}+ {1} n+1 terms. n. Substitute the expression Follow the given process to use this tool. a) Find the first 4 terms in the expansion of (1 + x/4) 8, giving each term in its simplest form. b) Use your expansion to estimate the value of (1.025) 8, giving your answer to 4 decimal places. In the binomial expansion of (2 - 5x) 20, find an expression for the coefficient of x 5. Find the Taylor series expansion of any function around a point using this online calculator. So if you were expanding (ax + b) 5: The power is 5 and the term number is whichever term you are interested in.

CCSS.Math: HSA.APR.C.5. Binomial Coefficient Calculator. Given that the coefficient of x 3 is 3 times that of x 2 in the expansion (2+3x) n, find the value of n. Difficult question involving the use of nCr formula. The exponents of a start with n, the power of the binomial, and decrease to 0.

Integration By Parts Calculator: Want to calculate the integration by parts of an expression in an easy way?Then you must go through the below sections of this page.

Binomial. The first term in the binomial is "x 2", the second term in "3", and the power n for this expansion is 6.

Binomial Expansion Calculator The binomial theorem is used to expand the binomials expression to any given power without direct multiplication. For any binomial expansion of (a+b) n, the coefficients for each term in the expansion are given by the nth row of Pascals triangle. Term Independent of x in Binomial Theorem Algebra > Binomial Theorem > Independent Term of x 8.

Algebra1help.com contains helpful tips on binomial expansion calculator with steps, complex and rational expressions and other math subjects. Here, the coefficients n C r are called binomial coefficients.

For example, if a binomial is raised to the power of 3, then looking at the 3rd row of Pascals triangle, the coefficients are 1, 3, 3 and 1. Binomial Expansion.

1 - Enter and edit the expression to expand and click "Enter Expression" then check what you have entered.

A binomial distribution is the probability of something happening in an event.

Now on to the binomial. In this way, using pascal triangle to get expansion of a binomial with any exponent. Enter required values and click the Calculate button to get the result with expansion using binomial theorem calculator. * (r)!) Example 7 : Find the 4th term in the expansion of (2x 3)5. The binomial theorem inspires something called the binomial distribution, by which we can quickly calculate how likely we are to win $30 (or equivalently, the likelihood the coin comes up heads 3 times). This is a very simple tool for Binomial Expansion Calculator. As we have explained above, we can get the expansion of (a + b) 4 and then we have to take positive and negative signs alternatively staring with positive sign for the first term.

The binomial theorem.

Whenever you need help on inverse functions or Expand and simplify polynomials. 1. Exponent of 0.

The following are the properties of the expansion (a + b) n used in the binomial series calculator. In each term, the sum of the exponents is n, the power to which the binomial is raised. k!]. n C r = (n!) Binomial Expansion Calculator to the power of: EXPAND: Computing Get this widget.

The binomial expansion calculator is used to solve mathematical problems such as expansion, series, series extension, and so on. This operation is built in to Take any function to get the binomial expansion. Step 2: Now click the button Expand to get the expansion. "=COMBIN (n, k)" where

An online binomial theorem calculator helps you to find the expanding binomials for the given binomial equation. The binomial coefficients ${n\choose k}$ that the above calculator compute are included in the binomial expansion Use of Pascals triangle to solve Binomial ExpansionInitially, the powers of x start at n and decrease by 1 in each term until it reaches 0.After that, the powers of y start at 0 and increase by one until it reaches n.Then, the n row of Pascal's triangle will be the expanded series' coefficients when the terms are arranged.More items Another interesting use of the binomial expansion is to calculate estimations of powers. In the expansion of a binomial term (a + b) raised to the power of n, we can write the general and middle terms based on the value of n. Before getting into the general and middle terms in binomial expansion, let us recall some basic facts about binomial theorem and expansion.. The binomial expansion formula is given by (a+b) n = k=0 to n (n!/ (n-k)! Firstly, write the expression as ( 1 + 2 x) Binomial Theorem Calculator Get detailed solutions to your math problems with our Binomial Theorem step-by-step calculator. Algebra. x 0 = 1. The binomial theorem widely used in statistics is simply a formula as below : ( x + a) n. =.

(2) 1 2 x = 2 y 2 = y 2 2 = 1 y 1 2 x. Created by Sal Khan. SolveMyMath's Taylor Series Expansion Calculator. Found the clue? Know the definition, explanation, terms and solved examples on binomial theorem and expansion. binomial_expand uses zip (range (1, len (coefficients)+1), coefficients) to get pairings of the each coefficient and its one-based index.

Find more Mathematics widgets in Wolfram|Alpha.

If a = -1, a "-" will be placed in front of the variable. The binomial expansion calculator is used to solve mathematical problems such as expansion, series, series extension, and so on.

Binomial Theorem - Challenging question with power unknown.