How do you factor completely: x^2 + 10x + 25?

Apr 2, 2018

${\left(x + 5\right)}^{2}$

Explanation:

$a {x}^{2} + b x + c$

Start by writing down all of the factors of c (25 in this case)
25 = 1*25; 25 = 5*5
now check, which of them might add up to, or have a difference of b (10 in this case)
$5 + 5 = 10$
so now we can insert these into the brackets:
$\left(x + 5\right) \left(x + 5\right)$
which is equivalent to ${\left(x + 5\right)}^{2}$