Question

Chứng minh: a³ + b³ = (a+b) ( ( a-b)²​ + ab)

Answer 1

VP: \(\left(a+b\right)\left[\left(a-b\right)^2+ab\right]=\left(a+b\right)\left(a^2-2ab+b^2+ab\right)\)

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

\(=a^3+b^3=VT\left(đpcm\right)\)

Answer 2

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

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

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

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

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

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