Question

Chứng minh (a - b)³ = (a - b)(a² + ab + b²) - 3ab(a - b)

Answer 1

Ta có: \(VP=\left(a-b\right)\left(a^2+ab+b^2\right)-3ab\left(a-b\right)\)

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

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

⇒ đpcm

Answer 2

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

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

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