SOLUTION: x^2-4xy+4y^2-z^2+8z-16. Factor completely. Should I group the first three? And then the second three? Help please!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: x^2-4xy+4y^2-z^2+8z-16. Factor completely. Should I group the first three? And then the second three? Help please!      Log On


   

Question 257120: x^2-4xy+4y^2-z^2+8z-16.
Factor completely.
Should I group the first three? And then the second three? Help please!
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the original problem:
x%5E2-4xy%2B4y%5E2-z%5E2%2B8z-16
step 1 - group the first 3 and the last 3 like this:
%28x%5E2-4xy%2B4y%5E2%29-%28z%5E2-8z%2B16%29
Notice we had to change the signs on the last 3 because we factored out a negative.
step 2 - factor the first group and the second group separately as
%28x-2y%29%5E2+-+%28z-4%29%5E2
step 3 - notice we now have difference of 2 squares, so we factor to get
%28x+-+2y+%2B+z+-+4%29%28x-2y+-z+%2B+4%29