Question

Simplify :x-³y-³(x-y)³​

Answer 1

Answer:

$\huge\boxed{x^3-y^3-(x-y)^3=3x^2y-3xy^2}$

Step-by-step explanation:

$x^3-y^3-(x-y)^3\qquad|\text{use}\ (a-b)^3=a^3-3a^2b+3ab^2-b^3\\\\=x^3-y^3-(x^3-3x^2y+3xy^2-y^3)\\\\=x^3-y^3-x^3+3x^2y-3xy^2+y^3\qquad|\text{combine like terms}\\\\=(x^3-x^3)+(-y^3+y^3)+3x^2y-3xy^2\\\\=3x^2y-3xy^2$