Answer
$x^2+12x+36=(x+6)^2$
Work Step by Step
We add the square of half of the coefficent of $x$ so that the result is a perfect square trinomial.
Co-efficient of $x = 12$
Half of 12 is $\frac{1}{2} \times 12= 6 $
Square of 6 is $6\times6=36$
We add 36 to $x^2+12x$ to make it a perfect square trinomial.
Hence it becomes $x^2+12x + 36$
Factored form-
$x^2+12x + 36$
$= x^2+6x+ 6x + 36$
$= x(x + 6) + 6(x+6)$ (Taking the common factors)
$= (x+6) (x+6)$ ( x+6 is taken common from both the terms)
$=(x+6)^2$
