Question

C=(x²-2xy+2y²)(x²+y²)-2x³y-3x³y²+2xy³

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Answer 1

\(C=\left(x^2-2xy+y^2\right)\left(x^2+y^2\right)-2x^3y-3x^3y^2+2xy^3\)

\(=\left(x^2+y^2\right)^2-2xy\left(x^2+y^2\right)-xy\left(2x^2+3x^2y+2y^2\right)\)

\(=\left(x^2+y^2\right)^2-xy\left(2x^2+2y^2+2x^2+3x^2y+2y^2\right)\)

\(=\left(x^2+y^2\right)^2-xy\left(4x^2+3x^2y+4y^2\right)\)

 

 

Answer 2