# How do you multiply 6a (a^2 + 2ab + b^2) ?

May 10, 2018

$6 {a}^{3} + 12 {a}^{2} b + 6 a {b}^{2}$

#### Explanation:

$6 a \left({a}^{2} + 2 a b + {b}^{2}\right)$

The distributive property is shown here:

Although the image has two terms inside the parenthesis rather than three terms in the question, we can apply it to this question.

The $\textcolor{b l u e}{6 a}$ multiplies to everything inside the parenthesis:
$\left(6 a \cdot {a}^{2}\right) + \left(6 a \cdot 2 a b\right) + \left(6 a \cdot {b}^{2}\right)$

Now simplify by multiplying:
$6 {a}^{3} + 12 {a}^{2} b + 6 a {b}^{2}$

Hope this helps!

May 10, 2018

$6 {a}^{3} + 12 {a}^{2} b + 6 a {b}^{2}$

#### Explanation:

$6 a \left({a}^{2} + 2 a b + {b}^{2}\right)$

Use the Distributive Property:
=$6 a \cdot {a}^{2} + 6 a \cdot 2 a b + 6 a \cdot {b}^{2}$
=$6 {a}^{3} + 12 {a}^{2} b + 6 a {b}^{2}$