ข้อ 8
ขอแสดงความเห็นเพิ่มเติม
\[\begin{array}{l}
f\left( {x + y} \right) = f\left( x \right) + f\left( y \right) + 4xy\\
geuss \Rightarrow \quad f\left( x \right) = a{x^2} + bx + c\\
f\left( {x + y} \right) = a{\left( {x + y} \right)^2} + b\left( {x + y} \right) + c\\
\quad \quad \quad \quad = a{x^2} + 2axy + a{y^2} + bx + by + c\\
sub \Rightarrow \\
a{x^2} + 2axy + a{y^2} + bx + by + c = a{x^2} + bx + c + a{y^2} + by + c + 4xy\\
then \Rightarrow \quad a = 2,c = 0\\
\Rightarrow f\left( x \right) = 2{x^2} + bx\\
\Rightarrow f\left( 1 \right) = 4\quad ,b = 2\\
\Rightarrow f\left( x \right) = 2{x^2} + 2x
\end{array}\]
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