Question

[Big City Boy]

Phân tích đa thức thành nhân tử: \(A=\left(a+b+c\right).\left(bc+ca+ab\right)-abc\)

Answer 1

[Thu Thao]

\(A=\left(a+b+c\right)\left(bc+ac+ab\right)-abc\)

\(=abc+b^2c+bc^2+a^2c+abc+ac^2+a^2b+ab^2+abc-abc\)

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

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

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

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

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