ANSWER :
The answer is B. y = (x + 4)^2 + 9
EXPLANATION :
From the problem, we have :
[tex]y=x^2+8x+25[/tex]Group the terms in which the constant term and the terms with variables are separated.
[tex]y=(x^2+8x)+(25)[/tex]add and subtract a variable m to the parenthesis to maintain equivalency.
[tex]y=(x^2+8x+m)+(25-m)[/tex]Calculate the value of m using b^2/4a^2 with a = 1 and b = 8
[tex]m=\frac{b^2}{4a^2}=\frac{8^2}{4(1^2)}=16[/tex]Then :
[tex]\begin{gathered} y=(x^2+8x+16)+(25-16) \\ y=(x^2+8x+16)+(9) \end{gathered}[/tex]The first parenthesis will be a perfect square trinomial.
Factor and simplify :
[tex]\begin{gathered} y=(x^2+8x+16)+9 \\ y=(x+4)^2+9 \end{gathered}[/tex]