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# Factor each of these fully

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Factor each of these fully

1. (a^2-6)^2 - (4a + 6)^2

2. (2m -3)^2 - (8m^2 - 4)^2

3. (17p^2 -26) - (8p^2 -4)^2

Guest Dec 20, 2017
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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

CPhill  Dec 20, 2017

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