verify that x³-y³-z³-3xyz = ½(x-y-z) [(x-y)²-(3-z)²-(z-y)²] . . plz ans. this wid explanaition ​

Question

verify that x³-y³-z³-3xyz = ½(x-y-z) [(x-y)²-(3-z)²-(z-y)²]
.
.
plz ans. this wid explanaition ​

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Rylee 6 months 2021-12-10T17:05:12+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-12-10T17:06:51+00:00

    Answer:

    First the formula is

    x^3+y^3+z^3-3xyz= (x+y+z) (x^2+y^2+z^2-xy-yz-zx)

    We need to prove the above equation is equal to this formula

    Solving RHS

    it is in the form (a-b)^2= a^2+b^2-2ab

    =1/2 (x+y+z) (x-y)^2-(3-z)^2-(z-y)^2

    =1/2 (x+y+z) [(x^2+y^2-2xy) (y^2+z^2-2yz) (z^2+x^2-2zx)]

    =1/2 (x+y+z) [(2x^2+y^2+2z^2-2xy-2yz-2zx)]

    In this u can see 2 is common lets take it outside

    =1/2 (x+y+z) 2[x^2+y^2+z^2-xy-yz-zx]

    In this 1/2 gets cancelled with the common 2

    =(x-y-z) [x^2+y^2+z^2-xy-yz-zx]

    Hence, it is appropriate with the formula

    x^3+y^3+z^3-3xyz.

    It is equal to =LHS

    Hence proved

    THANK YOU

    I HOPE IT HELPS

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