Question

a³ + b³ - (a² - 2ab + b²)(a - b)

Answer 1

\(a^3+b^3-\left(a^2-2ab+b^2\right)\left(a-b\right)\)

\(=a^3+b^3-\left(a-b\right)^2\left(a-b\right)\)

\(=a^3+b^3-\left(a-b\right)^3\)

\(=a^3+b^3-\left(a^3-3a^2b+3ab^2-b^3\right)\)

\(=a^3+b^3-a^3+3a^2b-3ab^2+b^3\)

\(=2b^3+3a^2b-3ab^2\)

\(=b\left(2b^2+3a^2-3ab\right)\)

Answer 2

\(=a^3+b^3-\left(a^3-b^3\right)\\ =a^3+b^3-a^3+b^3\\ =2b^3\)