Need Help with 3 Factoring Questions?

Question

Factor:
1) (p+2)^3 - (p-2)^3
2) m^2 - n^2 - 8n -16
3) (a-b)^4 - (a-b)^2

Any help or suggestions, would be appreciated

Answer 1

1)
Difference of cubes formula:
(x^3 - y^3) = (x - y)(x^2 + xy + y^2)

so...
[(p+2) - (p-2)][(p+2)^2 + (p+2)(p-2) + (p-2)^2]
(4)[(p^2 + 4p + 4) + (p^2 - 4) + (p^2 - 4p + 4)]
4(3p^2 + 4)

2)
That doesn't really factor. There are a few ways you can factor part of it, but the whole thing doesn't factor nicely.

3)
Use the difference of squares formula:
(a^2 - b^2) = (a - b)(a + b)

(a-b)^4 - (a-b)^2
[(a - b)^2 - (a - b)][(a - b)^2 + (a - b)]

Answer 2

#1
( (p+2) + (p-2)) ((p+2) + (p-2)) ((p+2) - (p-2))

#2:

m^2 -n^2 -8n -16
m^2 - (n^2 +8n +16) factor out -1
m^2 - (n +4)^2 n^2 +8n +16 factored is (n+4)^2
(m +(n+4)) (m - (n+4))

#3
((a-b)^2 - (a-b)) ((a-b)^2 + (a-b))

Answer 3

1) (p+2)^3 - (p-2)^3
= p^3+2p^2+4p +8= -(p^3-2p^2 +4p -8)
2p^3 + 8p = 2p(p^2+4)

2) m^2 - n^2 - 8n -16
=m^2-(n^2+8n+16)
= m^2-(n+4)^2
=(m-n-4)(m+n+4)

3) (a-b)^4 - (a-b)^2
=(a-b)^2[(a-b)^2 -1)
(a-b)(a+b)(a-b+1)(a-b-1)

Answer 4

(1) 4(3p^2+4)
(2) (m-n-4)(m+n+4)
(3) (a-b-1)(a-b)^2(a-b+1)
Please give me best answer thanks!