What is meant by a power of a binomial?

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What is meant by a power of a binomial?

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Answer 1 · 2015-08-29T18:32:27

The power of a binomial is the value of $n$ $n$ in the binomial expression ${(a + x)}^{n}$ $(a+x)^n$ .

Explanation:

For any value of $n$ $n$ , the $n^{th}$ $n^"th"$ power of a binomial is given by:

${(x + y)}^{n} = x^{n} + n x^{n - 1} y + \frac{n (n - 1)}{2} x^{n - 2} y^{2} + \dots + y^{n}$ $(x+y)^n=x^n +nx^(n-1)y +(n(n-1))/2x^(n-2)y^2 + … + y^n$

The general formula for the expansion is:

${(x + y)}^{n} = n \sum k = 0 \frac{n!}{(n - k)! k!} x^{n - k} y^{k}$ $(x+y)^n = sum_(k=0)^n (n!)/((n-k)!k!)x^(n-k)y^k$

The coefficients for varying $x$ $x$ and $y$ $y$ can be arranged to form Pascal's triangle.

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The $n^{th}$ $n^"th"$ row in the triangle gives the coefficients of the terms in the ${(n - 1)}^{th}$ $(n-1)^"th"$ power of the polynomial.

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What is meant by a power of a binomial?

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