# Is 4x^2 + 28x + 49 a perfect square trinomial and how do you factor it?

Jun 22, 2015

Yes it is.

$4 {x}^{2} + 28 x + 49 = {\left(2 x + 7\right)}^{2}$

#### Explanation:

All perfect square trinomials are of the form:

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

In this case $a = 2 x$ and $b = 7$ ...

$4 {x}^{2} + 28 x + 49$

$= {\left(2 x\right)}^{2} + \left(2 \cdot \left(2 x\right) \cdot 7\right) + {7}^{2}$

$= {\left(2 x + 7\right)}^{2}$