SOLUTION: Factor 625r^6-5p^6 The correct factorization is? thank you!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor 625r^6-5p^6 The correct factorization is? thank you!      Log On


   

Question 325024: Factor
625r^6-5p^6
The correct factorization is?
thank you!
Found 2 solutions by unlockmath, MathTherapy:
Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
The factor for this 625r^6-5p^6 is:
5(125r^6-p^6)
Now it can be factored more to get:
5(r^2-p^2)(25r^4+5r^2p^2+p^4)
Got it?
RJ

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Factor
625r^6-5p^6

5%28125r%5E6+-+p%5E6%29 ------ Dividing by GCF, 5
We can rewrite the expression as a difference of 2 cubes: 5[%285r%5E2%29%5E3+-+%28p%5E2%29%5E3]

Since a%5E3+-+b%5E3+=+%28a+-+b%29%28a%5E2+%2B+ab+%2B+b%5E2%29, %285r%5E2%29%5E3+-+%28p%5E2%29%5E3 = %285r%5E2+-+p%5E2%29%2825r%5E4+%2B+5p%5E2r%5E2+%2B+p%5E4%29

Therefore, the factors of 625r%5E6+-+5p%5E6 are: 5[highlight_green%28%285r%5E2+-+p%5E2%29%2825r%5E4+%2B+5p%5E2r%5E2+%2B+p%5E4%29%29]