How do you simplify (4x + 5)^2?

Mar 4, 2018

$= 16 {x}^{2} + 40 x + 25$

Explanation:

${\left(4 x + 5\right)}^{2}$

$= \left(4 x + 5\right) \left(4 x + 5\right)$

Distribute

$= \left(4 x\right) \left(4 x\right) + \left(4 x\right) \left(5\right) + \left(5\right) \left(4 x\right) + \left(5\right) \left(5\right)$

$= 16 {x}^{2} + 20 x + 20 x + 25$

$= 16 {x}^{2} + 40 x + 25$

Mar 4, 2018

$16 {x}^{2} + 40 x + 25$

Explanation:

This is a perfect square:

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

Plug in:

$16 {x}^{2} + 2 \cdot 4 x \cdot 5 + 25$

$16 {x}^{2} + 40 x + 25$

You could also write it out:

$\left(4 x + 5\right) \left(4 x + 5\right)$

$16 {x}^{2} + 20 x + 20 x + 25$

$16 {x}^{2} + 40 x + 25$