Answer: \(x^2+8x+16\)
Explanation:
A perfect square is an expression in the form
\((x+a)^2\)
which can be rewritten in a trinomial form:
\((x+a)^2 = (x+a)(x+a)=x^2 +ax+ax+a^2 = x^2 +2ax +a^2\) (1)
In this problem, we have the following trinomial:
\(x^2 + 8x +C\) (2)
with C unknown. By comparing (1) and (2), we see that
\(2a=8\\a^2 = C\)
from the first equation, we find
\(a=4\)
and substituting into the second one, we find
\(C=a^2=4^2=16\)
So, the perfect square trinomial form is
\(x^2+8x+16\)
