Multiple variable factoring + check an answer?

First question:

How do you factor when you have multiple variables?

Factor completely:

100a^{5}b - 36ab^{3}

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

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Second:

Factor completely:

m^{3}- 64

m^{3} - 64 = (m-4)(m^{2}+4m+16)

Is that correct?

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

Re: Multiple variable factoring + check an answer?

Hint :

$\displaystyle 100a^5b-36ab^3=ab\left(\left(10a^2\right)^2-(6b)^2\right)$

Re: Multiple variable factoring + check an answer?

Thank you! Princeps, can you explain or tell me what you did in the hint?

Re: Multiple variable factoring + check an answer?

Is it just simplifying? Because there are two 5a^{2} you then just square those -- like stating (5a^{2})(5a^{2})? And you get ten because there are 2 fives?

Re: Multiple variable factoring + check an answer?

Quote:

Originally Posted by

**Kibbygirl** Is it just simplifying? Because there are two 5a^{2} you then just square those -- like stating (5a^{2})(5a^{2})? And you get ten because there are 2 fives?

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