SOLUTION: I'm supposed to factor this: 6x^4y^4z^4-24x^5y^5z^3+18x^3y^3z^4

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Question 181481This question is from textbook
: I'm supposed to factor this:
6x^4y^4z^4-24x^5y^5z^3+18x^3y^3z^4
This question is from textbook

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I'm supposed to factor this:
6x%5E4y%5E4z%5E4-24x%5E5y%5E5z%5E3%2B18x%5E3y%5E3z%5E4
Do you plan to?
Look for the highest exponent of x, y and z, and factor it out. There's a 6 that's common to all 3 terms, too.
6x%5E4y%5E4z%5E4-24x%5E5y%5E5z%5E3%2B18x%5E3y%5E3z%5E4
=6x%5E3y%5E3z%5E3%2A%28xyz+-+4x%5E2y%5E2+%2B+3z%29
I think that's it.
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If you're unsure, you can do it bit at a time.
6x%5E4y%5E4z%5E4-24x%5E5y%5E5z%5E3%2B18x%5E3y%5E3z%5E4
Remove, say, the 6x
=6x%2A%28x%5E3y%5E4z%5E4+-+4x%5E4y%5E5z%5E3+%2B3+x%5E2y%5E3z%5E4%29
Then you see there's still an x in each term, so you factor out another one.
=6x%5E2%2A%28x%5E2y%5E4z%5E4+-+4x%5E3y%5E5z%5E3+%2B3+xy%5E3z%5E4%29
One more x
=6x%5E3%2A%28xy%5E4z%5E4+-+4x%5E2y%5E5z%5E3+%2B3+y%5E3z%5E4%29
The last term has no x, so we're done with x.
Do the same for y and z. Going one piece at a time makes it less likely to make an error.