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Math Help - Factorising algebraic expression

  1. #1
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    Factorising algebraic expression

    What method do I use to factorise 16x^4y + 2xy?

    The answer is 2xy(2x+1)(4x^2-2x+1)

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  2. #2
    Senior Member Stroodle's Avatar
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    One way to do it is to first take out the common factor of 2xy:

    2xy(8x^3+1)

    You can then see (or test) values of x that will make 8x^3+1=0

    In this case:

    P\left (-\frac{1}{2}\right )=0

    \therefore (2x+1) is a factor.

    Then if you divide 8x^3+1 by 2x+1 you'll get the quadratic factor.
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  3. #3
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    =2xy(8x^3+1)=2xy[(2x)^3+1]
    =2xy(2x+1)(4x^2-2x+1)
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  4. #4
    MHF Contributor

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    Lovemath is using the fact that x^3+ y^3)= (x+ y)(x^2- xy+ y^2).

    It is useful to know that, for all n, x^n- y^n= (x- y)(x^{n-1}+ x^{n-2}y+  \cdot\cdot\cdot+ xy^{n-2}+ y^{n-1})

    and, for all odd n, x^n+ y^n= (x+ y)(x^{n-1}- x^{n-1}y+ \cdot\cdot\cdot- xy^{n-1}+ y^n).
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