Question

Chứng minh rằng

a³+b³=(a+b)[(a-b)²+ab]

Answer 1

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

Áp dụng tính chất giao hoán nên :

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

\(\Rightarrow a^3+b^3=\left(a+b\right).\left[\left(a-b\right)^2+ab\right]\)

\(\RightarrowĐpcm\)

Answer 2

Ta có

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

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

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

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

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

\(\Rightarrow a^3+b^3=\left(a+b\right)\left[\left(a-b\right)^2+ab\right]\) (đpcm)

Answer 3

tach hang dang thuc hoac bien doi ve trai hoac ve faj