Factor each of these fully
please and thank you
1. (a^2-6)^2 - (4a + 6)^2
2. (2m -3)^2 - (8m^2 - 4)^2
3. (17p^2 -26) - (8p^2 -4)^2
1. (a^2-6)^2 - (4a + 6)^2
This is a difference of squares
[ (a^2 - 6) + (4a + 6)] [ [(a^2 - 6) - (4a + 6) ] =
[ a^2 + 4a] [ a^2 - 4a - 12 ] =
[a] [a + 4 ] [a - 6] [a + 2]
2. (2m -3)^2 - (8m^2 - 4)^2
Same thing
[ (2m - 3) + (8m^2 - 4) ] [(2m - 3) - (8m^2 - 4) ] =
[ 8m^2 + 2m - 7 ] [ -8m^2 + 2m + 1 ] =
[8m^2 + 2m - 7 ] [-1] [8m^2 - 2m - 1] =
[8m^2 + 2m - 7 ] [-1] [ 2m - 1] [ 4m + 1 ] =
- [8m^2 + 2m - 7 ] [ 2m - 1 ] [4m + 1]
3. (17p^2 -26) - (8p^2 -4)^2
(17p^2 - 26) - [ (8p^2 - 4) (8p^2 - 4) ] =
( 17p^2 - 26) - [ 64p^4 - 64p^2 + 16 ] =
[ - 64p^4 + 64p^2 + 17p^2 - 42 ] =
-64p^4 + 81p^2 - 42 ⇒ this is irreducible