SOLUTION: I need to completely factor 100-x^2y^2 and I came up with (50-xy)(50+xy). Is this correct?

Question 111936: I need to completely factor 100-x^2y^2 and I came up with (50-xy)(50+xy). Is this correct?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
You can always check these by multiplying your answers and to see if they match the original
given. In this case if you multiply the factors in your answer you will get:
.
2500 + 50xy -50xy - x^2y^2
.
The two middle terms cancel so your answer becomes 2500 - x^2y^2
.
Something is wrong. In this case you took a half of 100 (which is 50) as the first part of your
factors. You should have taken the square root of 100 (which is 10) so that your answer would
be (10 - xy)(10 + xy). If you multiply these two factors you get:
.
100 + 10xy - 10xy - x^2y^2
.
and when the two middle terms of this answer are canceled out because they are equal but
have opposite signs, you are left with:
.
100 - x^2y^2
.
which is the same form as you were originally given ... so it does check.
.
Hope this helps.
.
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