Question

What is meant by a power of a binomial?

Answer 1

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

Explanation:

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

`(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 = sum_(k=0)^n (n!)/((n-k)!k!)x^(n-k)y^k`

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

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