# How do I use Pascal's triangle to expand (2x + y)^4?

Jul 9, 2015

Write out the fifth row of Pascal's triangle and make the appropriate substitutions.

#### Explanation:

Pascal's triangle is

(from www.kidshonduras.com)

The numbers in the fifth row are 1, 4, 6, 4, 1.

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

${\left(x + y\right)}^{4} = {x}^{4} + 4 {x}^{3} y + 6 {x}^{2} {y}^{2} + 4 x {y}^{3} + {y}^{4}$

But our polynomial is ${\left(2 x + y\right)}^{4}$.

${\left(2 x + y\right)}^{4} = {\left(2 x\right)}^{4} + 4 {\left(2 x\right)}^{3} y + 6 {\left(2 x\right)}^{2} {y}^{2} + 4 \left(2 x\right) {y}^{3} + {y}^{4}$

${\left(2 x + y\right)}^{4} = 16 {x}^{4} + 32 {x}^{3} y + 24 {x}^{2} {y}^{2} + 8 x {y}^{3} + {y}^{4}$