The function $f(x)$ satisfies
\[f(x + y) = f(x) + f(y) + 2xy\]for all real numbers $x$ and $y.$  If $f(1) = 4,$ then find $f(8).$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The function $f(x)$ satisfies
\[f(x + y) = f(x) + f(y) + 2xy\]for all real numbers $x$ and $y.$  If $f(1) = 4,$ then find $f(8).$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
88
The function $f(x)$ satisfies
\[f(x + y) = f(x) + f(y) + 2xy\]for all real numbers $x$ and $y.$  If $f(1) = 4,$ then find $f(8).$
train