# factoring help

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• Apr 28th 2008, 02:25 PM
jesuslover
factoring help
Hello people! I need help with two math problems. They ask me to factor: 25a to the fourth - 14a squared b to the fourth + b to the eigth.

factor: 3a to the fourth + 48b to the fourth - 36a squared b squared.

I cannot figure out either one. With the first I need a number squared that equals 24, which is impossible of course, and the second I figured out I need a number squared that equals 20 which is also impossible (I figured that out with my own made-up equation.) Will someone show me how to solve these problems? I have tryed ever thing I can think of. Thank-you.
• Apr 28th 2008, 02:59 PM
Mathstud28
Quote:

Originally Posted by jesuslover
Hello people! I need help with two math problems. They ask me to factor: 25a to the fourth - 14a squared b to the fourth + b to the eigth.

factor: 3a to the fourth + 48b to the fourth - 36a squared b squared.

I cannot figure out either one. With the first I need a number squared that equals 24, which is impossible of course, and the second I figured out I need a number squared that equals 20 which is also impossible (I figured that out with my own made-up equation.) Will someone show me how to solve these problems? I have tryed ever thing I can think of. Thank-you.

\$\displaystyle 25a^4-14a^2b^4\$

Factor out a^2 to get \$\displaystyle a^2(25a^2-14b^4)\$
• Apr 29th 2008, 08:41 AM
sabyasachi
HI! HERE ARE THE SOLUTIONS:
1> 25a to the fourth - 14 a squared b to the fourth + b to the eight
= 25 a to the fourth - 10 a squared b to the fourth + b to the eight -
4 a squared b to the fourth
= square of (5 a squared -b to the fourth) - square of (2ab squared )
= ( 5 a2 + 2ab2 - b4)(5a2 - 2ab2 - b4)
2> 3a4 + 48b4 - 36a2b2
= 3(a4 - 12a2b2 + 16b4)
= 3 { a4 -8a2b2 + 16b4 - 4a2b2}
= 3 { ( a2-4b2)2 - (2ab)2
= 3 { (a2 -2ab -4b2)(a2 +2ab - 4b2)
= 3 (a2-2ab -4b2)(a2 + 2ab - 4b2)

got it!!!
• Apr 30th 2008, 08:39 AM
jesuslover
Hi! Thank-you for your help, but I decided to give it one last try last night and was able to figure it out. I'm sorry I bothered you guys. I really was stuck at the time. I need to learn to look back at the book when I'm stuck. or at least more closely. I'm sorry.
• Apr 30th 2008, 08:46 AM
janvdl
Quote:

Originally Posted by jesuslover
Hi! Thank-you for your help, but I decided to give it one last try last night and was able to figure it out. I'm sorry I bothered you guys. I really was stuck at the time. I need to learn to look back at the book when I'm stuck. or at least more closely. I'm sorry.

No problem... We are here to help and for someone as nice as you, we are more than happy to help again ;)