# How do you factor a perfect square trinomial  4a^2 − 10a − 25?

Jun 7, 2015

The equation #4a^2-10a-25 is not a perfect square trinomial. You will have to factor it with the quadratic formula.

Perfect square trinomials are the result of squaring binomials:

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

The last number in a perfect square trinomial cannot be negative because it is a squared number. For example:

${\left(3 x - 5\right)}^{2} = \left(3 x - 5\right) \left(3 x - 5\right)$

Foil $\left(3 x - 5\right) \left(3 x - 5\right)$.

$9 {x}^{2} - 15 x - 15 x + 25$ =

$9 {x}^{2} - 30 x + 25$