Question

How do you factor completely `2x^3y^4 − 8x^2y^3 + 6xy^2`?

Answer 1

`2x^3y^4-8x^2y^3+6xy^2=2xy^2(xy-3)(xy-1)`

Explanation:

Separate out the common factor `2xy^2` of the terms, then factor as a quadratic in `xy` as follows:

`2x^3y^4-8x^2y^3+6xy^2`

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

`=2xy^2((xy)^2-4(xy)+3)`

`=2xy^2(xy-3)(xy-1)`