x2-2xy+y2+3x-3y-4.

Question

Find the factor x2-2xy+y2+3x-3y-4.

Answer 1

x² - 2xy + y² + 3x - 3y - 4

(x - y)² + 3(x - y) - 4

[(x - y) + 4][(x - y) - 1]

Answer 2

The first three terms can be written make a perfect square trinomial.

 

(x - y)² = (x - y)(x - y) = x² - 2xy + y²

 

 

Then the last 3 terms becomes

 

3(x - y) - 4 = 3x - 3y - 4

 

 

So your factor form is

 

(x - y)² - 3(x - y) - 4

 

 

This is a substituted quadratic factor

 

where   (x - y) can be substituted for another variable.