Question

 Phân tích các đa thức sau thành nhân tử:

a) x ^ 3 - y ^ 3 + 2x - 2y

b) x ^ 2 + 8xy + 16y ^ 2 - 4z ^ 2

Answer 1

`a, x^3 - y^2 + 2x - 2y`
`= (x-y)(x^2 +xy+y^2) + 2(x-y)`
`= (x-y)(x^2+xy+y^2+2)`
`b, x^2 + 8xy + 16y^2 - 4z^2`
`= (x^2 + 8xy + 16y^2)- (2z)^2`
`= (x+4y)^2 - (2z)^2`
`=(x+4y-2z)(x+4y+2z)`

Answer 2

a.

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

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

b.

\(x^2+8xy+16y^2-4z^2=\left(x+4y\right)^2-\left(2z\right)^2\)

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