# How do I use Pascal's triangle to expand (x + 2)^5?

Jul 9, 2015

You write out the sixth row of Pascal's triangle and make the appropriate substitutions.

#### Explanation:

Pascal's triangle is

The numbers in the fifth row are 1, 5, 10, 10, 5, 1.

They are the coefficients of the terms in a fifth order polynomial.

${\left(x + y\right)}^{5} = {x}^{5} + 5 {x}^{4} y + 10 {x}^{3} {y}^{2} + 10 {x}^{2} {y}^{3} + 5 x {y}^{4} + {y}^{5}$

But our polynomial is ${\left(x + 2\right)}^{5}$.

(x+2)^5 = x^5 + 5x^4×2 + 10x^3×2^2 + 10x^2×2^3 + 5x×2^4 + 2^5

${\left(x + 2\right)}^{5} = {x}^{5} + 10 {x}^{4} + 40 {x}^{3} + 80 {x}^{2} + 80 x + 32$