# How do you factor 12x^2 + 60x + 75?

Oct 30, 2016

$12 {x}^{2} + 60 x + 75 = 3 {\left(2 x + 5\right)}^{2}$

#### Explanation:

Note that all of the terms are divisible by $3$, so separate that out as a scalar factor first:

$12 {x}^{2} + 60 x + 75 = 3 \left(4 {x}^{2} + 20 x + 25\right)$

Next note that $4 {x}^{2} = {\left(2 x\right)}^{2}$ and $25 = {5}^{2}$ are both perfect squares. So do we have a perfect square trinomial?

Let's try:

${\left(2 x + 5\right)}^{2} = {\left(2 x\right)}^{2} + 2 \left(2 x\right) \left(5\right) + {5}^{2} = 4 {x}^{2} + 20 x + 25$

$12 {x}^{2} + 60 x + 75 = 3 {\left(2 x + 5\right)}^{2}$