# How do you multiply (x + 5y)^3?

Jun 29, 2018

${x}^{3} + 15 {x}^{2} y + 75 x {y}^{2} + 125 {y}^{3}$

#### Explanation:

Given: ${\left(x + 5 y\right)}^{3}$.

Use the fact that ${\left(a + b\right)}^{3} = {a}^{3} + 3 {a}^{2} b + 3 a {b}^{2} + {b}^{3}$.

Letting $a = x , b = 5 y$, we get:

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

$= {x}^{3} + 15 {x}^{2} y + 3 x \cdot 25 {y}^{2} + 125 {y}^{3}$

$= {x}^{3} + 15 {x}^{2} y + 75 x {y}^{2} + 125 {y}^{3}$