Question

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

Answer 1

=sure google

Answer 2

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

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

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

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

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

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

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

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