Question

How do you factor `3x(x - 2y)^2- (x - 2y)^3`?

Answer 1

`2(x+y)(x-2y)^2`

Explanation:

Both terms are multiple of `(x-2y)^2`, so we can collect it:

`3x(x-2y)^2 - (x-2y)^3 = (x-2y)^2 [3x-(x-2y)]`

Simplifying the square brackets gives

`3x-(x-2y) = 3x-x+2y = 2x+2y=2(x+y)`

So, the whole expression equals `2(x+y)(x-2y)^2`