How do you factor x2−4y2−4x+4 by grouping?
1 Answer
Feb 1, 2017
Explanation:
The difference of squares identity can be written:
a2−b2=(a−b)(a+b)
By rearranging the given quadratic, we can recognise it as a difference of squares and hence factor it:
x2−4y2−4x+4=(x2−4x+4)−4y2
x2−4y2−4x+4=(x−2)2−(2y)2
x2−4y2−4x+4=((x−2)−2y)((x−2)+2y)
x2−4y2−4x+4=(x−2y−2)(x+2y−2)
