Question

Bài 1: Phân tích đa thức thành nhân tử

a) ax^2+ay^2-bx^2-by^2+b-a

b) ac^2-ad-bc^2+cd+bd-c^3

Answer 1

a, \(ax^2+ay^2-bx^2-by^2+b-a\)

\(=a\left(x^2+y^2\right)-b\left(x^2-y^2\right)-\left(a-b\right)\)

\(=\left(a-b\right)\left(x^2+y^2\right)-\left(a-b\right)\)

\(=\left(a-b\right)\left(x^2+y^2-1\right)\)

b, \(ac^2-ad-bc^2+cd+bd-c^3\)

\(=a\left(c^2-d\right)-\left(bc^2-bd\right)-\left(c^3-cd\right)\)

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

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