Question

Multiply x^{2} by x^{3}-2xy+y^{3} and find the value of the product for x=1, y=-1.

Answer 1

Identity used: x³+y³+z³−³xyz=(x+y+z)(x²+y²+z²−xy−yz−zx)

Now,(x+³y+³z)(x²+4y²+9z²−2xy−6yz−3zx)

=(x+2y+3z)(x2+(2y)2+(3z)2−x×2y−2y×3z−3z×x)

=x3+(2y)3+(3z)2−3×x×2y×3z

=x3+8y3+27z3−18xyz