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

1 Answer
Mar 26, 2018

Answer:

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!