Question

Make a perfect square trinomial: 25^2+__x+16

Answer 1

square(one length sides)

(x + a)*(x+a) = (x + a)^2

Answer 2

root 25 = 5
root 16 = 4

you want to add the value that corresponds to the expansion of
(a*x + b)^2 = (a*x + b) * (a*x + b)

Answer 3

a^2*x^2 + 2*(a*b)*x + b^2

Answer 4

You have
25*x^2+ __ x + 16

compare that to the expansion above
a^2*x^2 + 2*(a*b)*x + b^2

so, a=5 , b = 4, the middle value is 2*5*4 or 40