Answer
$x^{2}+16x+64= (x+8)^2$
Work Step by Step
We add the square of half of the co-efficent of $x$ so that the result is a perfect square trinomial.
Co-efficient of $x=16$
Half of 16 is $16×\frac{1}{2}=8$
Square of is $8×8=64$
We add 64 to $x^2+16x$ to make it a perfect square trinomial.
Hence it becomes $x^2+16x+64$
Factored form-
$x^2+16x+64$
$=x^2+8x+8x+64$
$=x(x+8)+8(x+8)$ (Taking the common factors)
$=(x+8)(x+8)$ ( $x+8$ is taken common from both the terms)
$=(x+8)^2$
