SOLUTION: Factor: 15 + 3y – 5x2 – x2y

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Question 76737: Factor: 15 + 3y – 5x2 – x2y
Found 2 solutions by Poohbear272, jim_thompson5910:
Answer by Poohbear272(22) About Me  (Show Source):
You can put this solution on YOUR website!
%283%2A5%29%2A%283%2A5%2F%283%2A5%29%2B3%2Ay%2A5%2Ax%2A2%2Ax%2A2%2Ay%2F%283%2A5%29%29
15%2A%283%2A5%2F15%2B3%2A5%2Ay%2Ay%2Ax%2Ax%2A2%2A2%2F15%29

15%2A%283%2A5%2F15%2B3%2A5%2Ay%5E2%2Ax%5E2%2A2%5E2%2F15%29
15%2A%283%2A5%2F%283%2A5%29%2B3%2A5%2A2%5E2%2Ay%5E2%2Ax%5E2%2F15%29
15%2A%283%2A5%2F15%2B3%2A5%2A2%5E2%2Ay%5E2%2Ax%5E2%2F%283%2A5%29%29
15%2A%283%2A5%2F%283%2A5%29%2B3%2A5%2A2%5E2%2Ay%5E2%2Ax%5E2%2F15%29
15%2A%283%2A5%2F%283%2A5%29%2B2%5E2%2A1%2A1%2Ay%5E2%2Ax%5E2%2F%281%2A1%29%29
15%2A%283%2A5%2F15%2B2%5E2%2Ay%5E2%2Ax%5E2%2F1%29
15%2A%283%2A5%2F%283%2A5%29%2B2%5E2%2Ay%5E2%2Ax%5E2%29
15%2A%283%2A5%2F15%2B4%2Ay%5E2%2Ax%5E2%29
15%2A%283%2A5%2F%283%2A5%29%2B4%2Ay%5E2%2Ax%5E2%29
15%2A%281%2A1%2F%281%2A1%29%2B4%2Ay%5E2%2Ax%5E2%29
15%2A%281%2F1%2B4%2Ay%5E2%2Ax%5E2%29
15%2A%281%2B4%2Ay%5E2%2Ax%5E2%29
15%2A%284%2Ay%5E2%2Ax%5E2%2B1%29 Answer
Good Luck!

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
15+%2B+3y+-+5x%5E2+-+x%5E2y+ Start with the given problem
%2815+%2B+3y%29+%2B+%28-+5x%5E2+-+x%5E2y%29+ group like terms
3%285+%2B+y%29+-x%5E2%285+%2B+y%29+ Factor out a 3 out of the first group. Factor out a -x%5E2 our of the second group.
Notice we have a common term of (5+y). If we let w=5+y we get
3w-x%5E2w Since we have a common term of w, we can combine these terms
%283-x%5E2%29w Combine like terms
%283-x%5E2%29%285%2By%29replace w with 5+y
So 15+%2B+3y+-+5x%5E2+-+x%5E2y+ factors to %283-x%5E2%29%285%2By%29


Check:
If we foil %283-x%5E2%29%285%2By%29 we should get 15+%2B+3y+-+5x%5E2+-+x%5E2y+ again.
%283-x%5E2%29%285%2By%29 foil
%283-x%5E2%29%285%2By%29=3%2A5%2B3y-5x%5E2-x%5E2y=15%2B3y-5x%5E2-x%5E2y so this supports our answer