# Multiple variable factoring + check an answer?

• Apr 24th 2012, 11:05 PM
Kibbygirl
Multiple variable factoring + check an answer?
First question:
How do you factor when you have multiple variables?

Factor completely:
100a5b - 36ab3

4 will factor into both 100 and 36. And ab will factor into both the variable parts?

----
Second:
Factor completely:
m3- 64

m3 - 64 = (m-4)(m2+4m+16)

Is that correct?
• Apr 24th 2012, 11:21 PM
biffboy
Re: Multiple variable factoring + check an answer?
Correct so expression= 4ab(25a^4-9b^2)= 4ab(5a^2-3b)(5a^2+3b)
You have the 2nd question correct
• Apr 24th 2012, 11:22 PM
princeps
Re: Multiple variable factoring + check an answer?
Hint :

$100a^5b-36ab^3=ab\left(\left(10a^2\right)^2-(6b)^2\right)$
• Apr 25th 2012, 07:22 AM
Kibbygirl
Re: Multiple variable factoring + check an answer?
Thank you! Princeps, can you explain or tell me what you did in the hint?
• Apr 25th 2012, 07:32 AM
Kibbygirl
Re: Multiple variable factoring + check an answer?
Is it just simplifying? Because there are two 5a2 you then just square those -- like stating (5a2)(5a2)? And you get ten because there are 2 fives?
• Apr 25th 2012, 07:53 AM
princeps
Re: Multiple variable factoring + check an answer?
Quote:

Originally Posted by Kibbygirl
Is it just simplifying? Because there are two 5a2 you then just square those -- like stating (5a2)(5a2)? And you get ten because there are 2 fives?

$10^2 \cdot a^4 \cdot (ab)-6^2\cdot b^2\cdot(ab)=ab\left(10^2a^4-6^2b^2\right)$