# How do you factor completely: 16x^2 + 40x + 25?

Jul 24, 2015

This is recognisable as a perfect square trinomial:

$16 {x}^{2} + 40 x + 25 = {\left(4 x + 5\right)}^{2}$

#### Explanation:

Perfect square trinomials are of the form:

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

In our case $a = 4 x$ and $b = 5$ ...

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

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

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