Question

Phân tích đa thức

a) ( a + b + c)³ – a³ – b³ – c³

Answer 1

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

\(=a^3+b^3+c^3+3a^2b+3ab^2+3b^2c+3bc^2+3c^2a+3ca^2+6abc-a^3-b^3-c^3\)

\(=3a^2b+3ab^2+3b^2c+3bc^2+3c^2a+3ca^2+6abc\)

\(=3\left(abc+a^2b+ca^2+c^2a+b^2c+ab^2+abc+bc^2\right)\)

\(=3\left[ab\left(a+c\right)+ac\left(a+c\right)+b^2\left(a+c\right)+bc\left(a+c\right)\right]\)

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

\(=3\left(a+c\right)\left[a\left(b+c\right)+b\left(b+c\right)\right]\)

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

Chúc bạn học tốt!!!