Question

How do you factor `3x^(6n) y^2 - 39x^(3n) y^2 +120y^2`?

Answer 1

`3y^2(x^(3n) - 5)(x^(3n) - 8)`

Explanation:

Let 3y^2 be common factor -->
`f(x) = 3y^2(x^(6n) - 13x^(3n) + 40)`
Call `x^(3n) = X`. Factor the quadratic trinomial in X -->
`X^2 - 13X + 40.`
Find 2 numbers knowing sum (-13) and product (4).
They are -5 and -8.

`f(x) = 3y^2(X - 5)(X - 8) = 3y^2(x^(3n) - 5)(x^(3n) - 8)`