Question

Chứng minh

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

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

Answer 1

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

Biến đổi VT ta có :

+) \(a^3+b^3+c^3=ab+bc+ca\)

\(\Leftrightarrow3a^3+3b^3+3c^3=3ab+3bc+3ca\)

\(\Rightarrow\left(a-b\right)^3+\left(b-c\right)^3+\left(c-a\right)^3=0\)

\(\Rightarrow a=b=c\)

< => VT = VP 

=> đpcm

Answer 2

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

                                                              \(=a^3+b^3=VT\)