Factorize 8x3 - y3-12x2y+6xy2

(2x - y) ^3.

Step-by-step explanation:

8x^3 - y^3 - 12x^2y + 6xy^2

Looks like this is a perfect cube with first term = cube root of 8x^3 and the last term = cube root of - y^3. That is (2x - y) ^3.

Let's expand it:

(2x - y) ^3

= (2x - y) (2x - y) ^2

= (2x - y) (4x^2 - 4xy + y^2)

= 8x^3 - 8x^2y + 2xy^2 - 4x^2y + 4xy^2 - y^3

= 8x^3 - 12x^2y + 6xy^2 - y^3 which is the given expression.