# Factorize 25x^2+60x+36?

Jul 26, 2016

$25 {x}^{2} + 60 x + 36 = {\left(5 x + 6\right)}^{2}$

#### Explanation:

In $25 {x}^{2} + 60 x + 36$, the first and third term are complete square as $25 {x}^{2} = {\left(5 x\right)}^{2}$ and $36 = {6}^{2}$ and middle term is double the product of $5 x$ and $3$ i.e. $2 \times 5 x \times 6 = 60 x$

Hence using the identity ${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

$25 {x}^{2} + 60 x + 36$

= ${\left(5 x\right)}^{2} + 2 \times 5 x \times 6 x + {6}^{2}$

= ${\left(5 x + 6\right)}^{2}$