# What is meant by a power of a binomial?

Aug 29, 2015

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

#### Explanation:

For any value of $n$, the ${n}^{\text{th}}$ 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 ${n}^{\text{th}}$ row in the triangle gives the coefficients of the terms in the ${\left(n - 1\right)}^{\text{th}}$ power of the polynomial.