Question

Phân tích các đa thức thành nhân tử 

a, 8x+4x^2-12xy

b,  5x^3-10x^2+5x

c,   x^3+x^2y-xy^2-y^3

d,   x^2-8x-9

Answer 1

a) Ta có: \(8x+4x^2-12xy\)

\(=4x\left(2+x-3y\right)\)

b) Ta có: \(5x^3-10x^2+5x\)

\(=5x\left(x^2-2x+1\right)\)

\(=5x\left(x-1\right)^2\)

c) Ta có: \(x^3+x^2y-xy^2-y^3\)

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

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

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

d) Ta có: \(x^2-8x-9\)

\(=x^2-9x+x-9\)

\(=\left(x-9\right)\left(x+1\right)\)

Answer 2

a. `8x+4x^2-12xy=4x(2+x-3y)`

b) `5x^3-10x^2+5x=5x(x^2-2x+1)`

c) `x^3+x^2y-xy^2-y^3=x^2(x+y)-y^2(x+y)=(x+y)(x^2-y^2)=(x+y)^2 (x-y)`

d) `x^2-8x-9=(x^2-2.x.4+4^2)-25=(x-4)^2-5^2=(x+1)(x-9)`