Question

Find the factor: x2 - 2xy + y2 + 3x - 3y + 4 = 0

Answer 1

Answer:

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

Step-by-step explanation:

x²-2xy + y² + 3x - 3y -4

 According the formula for (a-b)² = a²-2ab + b²

This fits the first part of your equation if a=x and b=y

 x²-2xy+y² = (x-y)²

 So we have:

(x-y)² + 3x- 3y - 4

 You can factor a 3 out of the 3x-3y giving 3(x-y)

Giving:

 (x-y)² + 3(x-y) -4

 What we have is actually a quadratic equation of the form

ax² + bx + c   where   x = (x-y)

 represent x-y ...   Let  z = x-y    so you have:

 z² +3z -4

The factors of -4 that add to 3 are (4)(-1) so

 z² + 3z - 4

= (z+4)(z-1)

 But z = x-y   so we have:

 (x-y+4)(x-y-1)