Question

C/minh: \(\left(a+b\right)^3=a^3+b^3+3ab\left(a+b\right)\)

Answer 1

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

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

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

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

Vậy \(\left(a+b\right)^3\)\(=a^3+b^3+3ab\left(a+b\right)\)(đpcm)

Answer 2

Cách khác :

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

\(\Leftrightarrow a^3+3a^2b+3ab^2+b^2-a^3-b^3-3a^2b-3ab^2=0\)

\(\Leftrightarrow0=0\left(luôn-đúng\right)\)

\(\Rightarrowđpcm\)