SOLUTION: How do you factor 3r-3k+3r^2-3k^2? My book shows the answer as 3(r-k)(1+r+k) but I can't figure out how to arrive at that answer. I also need help on factoring m^2-p^2+2m+2p.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you factor 3r-3k+3r^2-3k^2? My book shows the answer as 3(r-k)(1+r+k) but I can't figure out how to arrive at that answer. I also need help on factoring m^2-p^2+2m+2p.      Log On


   

Question 516243: How do you factor 3r-3k+3r^2-3k^2? My book shows the answer as 3(r-k)(1+r+k) but I can't figure out how to arrive at that answer. I also need help on factoring m^2-p^2+2m+2p.
Found 2 solutions by mananth, gc2000:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
3r-3k+3r^2-3k^2
3(r-k)+3(r^2-k^2)
3(r-k)+3(r+k)(r-k)
3(r-k)(1+3r+k)
---
m^2-p^2+2m+2p
(m+p)(m-p)+2(m+p)
(m+p)(m-p+2)
m.ananth@hotmail.ca

Answer by gc2000(22) About Me  (Show Source):
You can put this solution on YOUR website!
Here are the steps, and you'll need to know that a^2 - b^2 = (a + b)(a - b)
3r - 3k + 3r^2 - 3k^2
[3 comes out of each difference]
3(r-k) + 3(r^2 - k^2)
[apply: a^2 - b^2 = (a + b)(a - b)]
3(r-k) + 3(r + k)(r - k)
[one more thing to factor: 3(r - k)]
(3(r - k))(1 + (r + k))
[some parentheses were only included for clarification, and aren't needed]
3(r - k)(1 + r + k)

m^2 - p^2 + 2m + 2p
[apply: a^2 - b^2 = (a + b)(a - b)]
(m + p)(m - p) + 2(m + p)
[factor out "(m + p)"]
(m + p)(m - p + 2)