# How do you multiply (2b+5a)^2?

Dec 21, 2016

$4 {b}^{2} + 20 a b + 25 {a}^{2}$

#### Explanation:

We can expand this expression as:

${\left(2 b + 5 a\right)}^{2} \to \left(2 b + 5 a\right) \left(2 b + 5 a\right)$

Now we can cross multiple the terms in each set of parenthesis:

$\left(2 b + 5 a\right) \left(2 b + 5 a\right) \to$

$\left(2 b \cdot 2 b\right) + \left(2 b \cdot 5 a\right) + \left(5 a \cdot 2 b\right) + \left(5 a \cdot 5 a\right) \to$

$4 {b}^{2} + 10 a b + 10 a b + 25 {a}^{2}$

Next we can add like terms:

$4 {b}^{2} + \left(10 + 10\right) a b + 25 {a}^{2}$

$4 {b}^{2} + 20 a b + 25 {a}^{2}$