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 $f(8).$
Question:
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 $f(8).$
Answer:
Let's think step by step.

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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 $f(8).$
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