Question

Phân tích đa thức thành nhân tử:a)8x^3+27y^3-8x-12y b)x^3-4x^2-12x+27

Answer 1

`(a):8x^{3}+27y^{3}-8x-12y`

`=(2x)^{3}+(3y)^{3}-4(2x+3y)`

`=(2x+3y)(4x^{2}-6xy+9y^{2})-4(2x+3y)`

`=(2x+3y)(4x^{2}-6xy+9y^{2}-4)`

`(b):x^{3}-4x^{2}-12x+27`

`=(x^{3}+3^{3})-(4x^{2}+12x)`

`=(x+3)(x^{2}-3x+9)-4x(x+3)`

`=(x+3)(x^{2}-3x+9-4x)`

`=(x+3)(x^{2}-7x+9)`

Answer 2

\(a,=\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)-4\left(2x+3y\right)\\ =\left(2x+3y\right)\left(4x^2-6xy+9y^2-4\right)\\ b,=\left(x^3+27\right)-4x\left(x+3\right)\\ =\left(x+3\right)\left(x^2-3x+9\right)-4x\left(x+3\right)\\ =\left(x+3\right)\left(x^2-3x+9-4x\right)\\ =\left(x+3\right)\left(x^2-7x+9\right)\)

Answer 3

`a, (2x+3y)(4x^2 - 6xy + 9y^2) - 4(2x+3y)`

`= (2x+3y)(4x^2 - 6xy + 9y^2-4)`

`b, (x+3)(x^2 - 3x + 9) - 4x(x+3)`

`= (x+3)(x^2 - 7x + 9)`