# How do you factor the expression 49y^2 + 112y + 64?

Jan 11, 2016

$49 {y}^{2} + 112 y + 64 = {\left(7 y + 8\right)}^{2}$

#### Explanation:

$49 {y}^{2} + 112 y + 64 = {7}^{2} {y}^{2} + 2 \cdot 7 \cdot 8 y + {8}^{2} =$
$= {\left(7 y\right)}^{2} + 2 \cdot 7 \cdot 8 y + {8}^{2}$

Use the Square of a binomial rule

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

with:

$a = 7 y$
$b = 8$