a)\(\Rightarrow A\left(a+b\right)=a^3+b^3\)
\(\Rightarrow A\left(a+b\right)=\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(\Rightarrow A=a^2-ab+b^2\)
b) \(\Rightarrow\left(4x^2-4xy+y^2\right)2xy=A\left(y^2-4x^2\right)\)
\(\Rightarrow2xy\left(y-2x\right)^2=A\left(y-2x\right)\left(y+2x\right)\)
\(\Rightarrow A\left(y+2x\right)=2xy\left(y-2x\right)\)
\(\Rightarrow A=\frac{2xy\left(y-2x\right)}{y+2x}\)