Question

pt đa thức ab(a+b)-bc(b+c)-ac(c-a)

Answer 1

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

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

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

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

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

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

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

Answer 2

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