Answer
$(4x+5)^{2} $
Work Step by Step
In accordance with the rules of factoring trinomials, we need to find two integers whose product is $16(25)=400$ and whose sum is $40$. A little searching determines that these numbers are $20$ and $20$. Therefore, we can express the middle term, $40x$, as $(20x+20x)$ and proceed to factoring by grouping:
$16x^{2}+40x+25$
=$16x^{2}+20x+20x+25$
=$4x(4x+5)+5(4x+5)$
=$(4x+5)(4x+5)$
=$(4x+5)^{2}$
