Question

[Nguyen Ha Vi]

Rut gon :

a(b^2+c^2+bc^2) + b(c^2+a^2+ac) + c(a^2+b^2+ab)

Thoi gian gap rut mn giup mk nhanh nha ! thanks trc

Answer 1

[Le Thi Khanh Huyen]

Ta có :

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

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

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

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

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

Answer 2

[Nguyen Ha Vi]

Thanks rat nhieu