Question

CMR: \(\left(a+b\right)^3-\left(a-b\right)^3-2b^3=6a^2b\)

Answer 1

ta có:(a+b)³-(a-b)³-2b³

^{=a3+3a2b+3ab2+b3-(a3-3a2b+3ab2-b3)-2b3}

^{=(a3-a3)+(3a2b+3a2b)+(3ab2-3ab2)+(b3+b3-2b3)}

^=6a2b(đpcm)

Answer 2

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

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

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

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

\(=6a^2b.\)

\(\Rightarrow\left(a+b\right)^3-\left(a-b\right)^3-2b^3=6a^2b\left(đpcm\right).\)

Chúc bạn học tốt!