Question

Answer 1

e: \(=x^3-3x^2y+3xy^2-y^3\)

f: \(=\dfrac{1}{2}x^2y^2\left(4x^2-y^2\right)=2x^4y^2-\dfrac{1}{2}x^2y^4\)

Answer 2

\(e,\left(x^2-2xy+y^2\right).\left(x-y\right)\)

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

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

\(f,\dfrac{1}{2}x^2y^2.\left(2x+y\right).\left(2x-y\right)\)

\(=\left(x^3y^2+\dfrac{1}{2}x^2y^3\right).\left(2x-y\right)\)

\(=2x^4y^2-\dfrac{1}{2}x^2y^4\)