SOLUTION: Factorize completely {{{ (2x^2 + xy -y^2) + 2x - y }}}

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Question 824626: Factorize completely
+%282x%5E2+%2B+xy+-y%5E2%29+%2B+2x+-+y+
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
+%282x%5E2+%2B+xy+-y%5E2%29+%2B+2x+-+y+
This can be factored using factoring by grouping. And the expression already has the first group (in the parentheses). So we group the rest of the expression...
+%282x%5E2+%2B+xy+-y%5E2%29+%2B+%282x+-+y%29+
... and factor each group. The first group is a trinomial which factors. The second group can only be factored by factoring out a 1 (or -1):
+%282x-y%29%28x%2By%29+%2B+1%2A%282x+-+y%29+
As we can see, each group now has a common factor, 2x-y. So we can factor that out of each group:
+%282x-y%29%28%28x%2By%29+%2B+1%29+
or just
+%282x-y%29%28x%2By+%2B+1%29+