SOLUTION: factor completely: a^2p^2 + q^2-p^2 - a^2q^2 thank you

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Question 545464: factor completely: a^2p^2 + q^2-p^2 - a^2q^2





thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
factor completely:
a%5E2p%5E2+%2B+q%5E2-p%5E2+-+a%5E2q%5E2
Re group this as follows
%28a%5E2p%5E2+-+p%5E2%29%2B%28q%5E2+-+aq%5E2%29
factor out the common term
p%5E2%28a%5E2+-+1%29+%2B+q%5E2%281+-+a%5E2%29
We want to change the sign of (1 - a^2), so change the sign of q^2, and we have
p%5E2%28a%5E2+-+1%29+-+q%5E2%28a%5E2+-+1%29
Factor out (a^2 - 1) and we have
%28a%5E2-1%29%28p%5E2-q%5E2%29