Divide (x^5 -y ^5 ) by (x-y) using the method of long division.​

Question

Divide (x^5
-y
^5
) by (x-y) using the method of long division.​

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Aubrey 18 mins 2021-11-23T08:27:14+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-11-23T08:29:01+00:00

    Long Division Method :

     \red{\frac{ (x^{5} - y^{5})}{(x-y)}}

    Q(x)=x⁴+y+y²+xy³+y⁴

    x-y|x⁵-y⁵|

    ****x⁵-x⁴y

    ___________

    *** x⁴y +0

    *** x⁴y-x³y²

    ___________

    ***** x³y²+0

    ***** x³y²-x²y³

    ____________

    ******x²y³+0

    ******x²y³-xy⁴

    _____________

    ****** xy⁴-y⁵

    *******xy⁴-y⁵

    _____________

    ********(0)

    Dividend = x⁵ y⁵

    Divisor = x-y

    Quotient = x⁴+y+y²+xy³+y⁴

    Remainder = 0

    Therefore.,

     \red{\frac{(x^{5} - y^{5})}{(x-y)}}

     \green{ = x^{4}+x^{3}y+x^{2}y^{2}+xy^{3}+y^{4}}

    •••♪

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