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How do I factor this problem `-105m^6n+28m^5n^2+21m^4n^3`

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monique06 | Valedictorian

Posted May 11, 2013 at 4:48 PM via web

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How do I factor this problem

`-105m^6n+28m^5n^2+21m^4n^3`

3 Answers | Add Yours

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oldnick | Valedictorian

Posted May 12, 2013 at 5:01 AM (Answer #3)

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`-105m^6n+28m^5n^2+21m^4n^3` `=7m^4n(-15m^2+4mn+3n^2)=` `-7m^4n(15m^2-4mn-3n^2)=` `-7m^4n(15m^2+5mn -9mn-3n^2)=`

`-7m^4n[5m(3m+n)-3n(3m+n)]=` `-7m^4n(5m-3n)(3m+n)`

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pramodpandey | College Teacher | Valedictorian

Posted May 17, 2013 at 5:19 AM (Answer #5)

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We have given

`-105m^6n+28m^5n^2+21m^4n^3`

`HCF (105,28,21)=7`

`HCF (m^6n,m^5n^2,m^4n^3)=m^4n`

`Thus` factor out `7m^4n`  from the given expression

`-7m^4n(15m^2-4mn-3n^2)`

splitting the middle term ,in the bracket

`-7m^4n(15m^2-9mn+5mn-3n^2)`

`-7m^4n(3m(5m-3n)+n(5m-3n))`

`-7m^4n(5m-3n)((3m+n)`

which is required facors.

Sources:

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monique06 | Valedictorian

Posted May 11, 2013 at 6:26 PM (Answer #2)

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No. the answer is -7m^4n(3m+n)(5m-3n)

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