Multiple variable factoring + check an answer?

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April 24th 2012, 10:05 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?

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Second:
Factor completely:
m³- 64

m³ - 64 = (m-4)(m²+4m+16)

Is that correct?
April 24th 2012, 10:21 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
April 24th 2012, 10:22 PM
princeps

Re: Multiple variable factoring + check an answer?

Hint :

$100a^5b-36ab^3=ab\left(\left(10a^2\right)^2-(6b)^2\right)$
April 25th 2012, 06:22 AM
Kibbygirl

Re: Multiple variable factoring + check an answer?

Thank you! Princeps, can you explain or tell me what you did in the hint?
April 25th 2012, 06:32 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?
April 25th 2012, 06:53 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?

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

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