\(\left\{{}\begin{matrix}f\left(x\right)=ax^3+bx^2+cx+d\\a;b;c;d\in Z;b=3a+c\end{matrix}\right.\) \(\begin{matrix}\left(1\right)\\\left(2\right)\end{matrix}\)
\(\left(1\right)\Rightarrow\left\{{}\begin{matrix}f\left(1\right)=a+b+c+d\\f\left(-2\right)=-8a+4b-2c+d\end{matrix}\right.\)
=>\(A=f\left(1\right).f\left(-2\right)=\left(a+b+c+d\right)\left(-8a+4b-2c+d\right)\)(3)
từ (2)và (3) \(\Leftrightarrow A=\left(a+b+c+d\right)\left(-8a+b+3\left(3a+c\right)-2c+d\right)\)
\(A=\left(a+b+c+d\right)\left(a+b+c+d\right)=\left(a+b+c+d\right)^2\) => dpcm
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