find the factor

Question

find the factor
x2–2xy+y2+3x–3y–4

Answer 1

x² - 2xy + y² + 3x - 3y- 4

 

To factor this, let's first group the terms and see if this will help with factoring.

(x² - 2xy + y²) + (3x - 3y) - 4

(x-y)² + 3(x-y) - 4

 

You might see that this really looks like a quadratic.  If you don't, let's set w = x-y.

Then w² + 3w - 4

We can factor this.

(w+4)(w-1)

And since w=x-y, we have

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

 

Hope this helps.