Question

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

Answer 1

The factored form is `(x-3y)(x+y)`.

Explanation:

You can treat it like a quadratic, where instead of constant numbers, there are `y` terms.

First, find two numbers that multiply to `-3` (the `c` value of the "quadratic") and add up to `-2` (the `b` value of the "quadratic").

These two numbers are `-3` and `1`. Split the middle term into these two numbers. Then, factor the first two and last two terms separately, then combine them:

`color(white)=x^2-2xy-3y^2`

`=x^2+xy-3xy-3y^2`

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

`=color(red)x(x+y)color(blue)-color(blue)(3y)(x+y)`

`=(color(red)xcolor(blue)-color(blue)(3y))(x+y)`

This is the factored form. Hope this helped!