SOLUTION: Factor fully (17p^2-26)^2-(8p^2-4)^2

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Question 1131330: Factor fully (17p^2-26)^2-(8p^2-4)^2
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Factor fully
%2817p%5E2-26%29%5E2-%288p%5E2-4%29%5E2+
289+p%5E4+-+884+p%5E2+%2B+676-%2864+p%5E4+-+64+p%5E2+%2B+16%29
289+p%5E4+-+884+p%5E2+%2B+676-64+p%5E4+%2B64+p%5E2+-16
225+p%5E4+-+820+p%5E2+%2B+660++
5%2845p%5E4+-+164+p%5E2+%2B+132%29++
5%2845p%5E4+-+54+p%5E2-110p%5E2+%2B+132%29++
5%28%2845p%5E4+-110p%5E2%29+-+%2854+p%5E2-+132%29%29++
5%285p%5E2%289p%5E2+-22%29+-+6%289+p%5E2-+22%29%29++
5+%289p%5E2+-+22%29+%285p%5E2+-+6%29

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Factor fully (17p^2-26)^2-(8p^2-4)^2
It's TOTALLY UNNECESSARY to FOIL the 2 BINOMIALS

It's a DIFFERENCE of TWO SQUARES, and is easy as:

%2817p%5E2+-+26%29%5E2+-+%288p%5E2+-+4%29%5E2

%28%2817p%5E2+-+26%29+-+%288p%5E2+-+4%29%29%28%2817p%5E2+-+26%29+%2B+%288p%5E2+-+4%29%29 ------ Applying matrix%281%2C3%2C+a%5E2+-+b%5E2%2C+%22=%22%2C+%28a+-+b%29%28a+%2B+b%29%29

%2817p%5E2+-+26+-+8p%5E2+%2B+4%29%2817p%5E2+-+26+%2B+8p%5E2+-+4%29%29

%289p%5E2+-+22%29%2825p%5E2+-+30%29

%289p%5E2+-+22%295%285p%5E2+-+6%29%29 ------ Factoring out GCF, 5, from the 2nd BINOMIAL

highlight_green%285%289p%5E2+-+22%29%285p%5E2+-+6%29%29%29