Is 4a^2 − 10a + 25 a perfect square trinomial and how do you factor it?

Jun 11, 2015

$4 {a}^{2} - 10 a + 25$ is a perfect square trinomial with factors ${\left(2 a - 5\right)}^{2}$

Explanation:

Since a perfect square trinomial has the form
$\textcolor{w h i t e}{\text{XXXX}}$${\left(p + q\right)}^{2} = {p}^{2} + 2 p q + {q}^{2}$

If $4 {a}^{2} - 10 a + 25$ is to be a perfect square
$\textcolor{w h i t e}{\text{XXXX}}$${p}^{2} = 4 {a}^{2} \rightarrow p = \pm 2 a$
and
$\textcolor{w h i t e}{\text{XXXX}}$${q}^{2} = 25 \rightarrow q = \pm 5$

Picking $p = 2 a$ and $q = - 5$
results in a middle term of $- 10 a$
as required to be a perfect square.
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