# How do you factor 49a^2+28ab+4b^2 using the perfect squares formula?

Mar 16, 2017

See the entire solution process below:

#### Explanation:

The perfect squares formula states:

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

For this problem:

If ${x}^{2} = 49 {a}^{2}$ then:

$\sqrt{{x}^{2}} = \pm \sqrt{49 {a}^{2}}$

$x = \pm 7 a$

If ${y}^{2} = 4 {b}^{2}$ then:

$\sqrt{{y}^{2}} = \pm \sqrt{4 {b}^{2}}$

$y = \pm 2 b$

Substituting these into the factors in the formula gives:

$\left(7 a + 2 b\right) \left(7 a + 2 b\right)$

Or

$\left(- 7 a - 2 b\right) \left(- 7 a - 2 b\right)$