Question

phân tích đa thức thành nhân tử B=a(b^2-c^2)+b(c^2-a^2)+c(a^2-b^2)

Answer 1

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

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

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

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

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

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

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