+0  
 
0
273
1
avatar

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

 Dec 20, 2017
 #1
avatar+94558 
+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

 

 

 

cool cool cool

 Dec 20, 2017

22 Online Users

avatar
avatar
avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.