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Math Help - Factoring Question

  1. #1
    Newbie pinky&thebrain's Avatar
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    Factoring Question

    I am having a hard time factoring the following:

    12a^6b^4c^2 + 15a^2b^4c^6

    Thanks for the help
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  2. #2
    Junior Member
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    Are you using carrots ^ to mean multiplication or do you really mean that those are all powers of powers of powers?
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  3. #3
    MHF Contributor
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    12a^6b^4c^2 + 15a^2b^4c^6

    Rewriting that,
    12(a^6)(b^4)(c^2) + 15(a^2)(b^4)(c^6)

    If that is the intention, then,

    We factor the numerical coefficients first.
    12 and 15
    There is a factor of 3 that is common to both.
    So, (3 )(4 and 5)

    Then the variable a.
    a^6 and a^2.
    There is a factor of a^2 that is common to both.
    So, (a^2)(a^4 and 1).

    Then the variable b.
    b^4 and b^4.
    b^4 is common to both.
    So, (b^4)(1 and 1).

    Then the variable c.
    c^2 and c^6.
    There is a factor of c^2 that is common to both.
    So, (c^2)(1 and c^4)

    Hence,
    12(a^6)(b^4)(c^2) + 15(a^2)(b^4)(c^6)
    = (3*a^2 *b^4 *c^2)(4*a^4*1*1 +5*1*1*c^4)
    = (3a^2 b^4 c^2)(4a^4 +5c^4) ....answer.
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