suppose that when you factor 4t^6-r^10, you get (2t^x+r^y)(2t^x-r^y). determine the sum of t and r.

Question

suppose that when you factor 4t^6-r^10, you get (2t^x+r^y)(2t^x-r^y). determine the sum of t and r.

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Thiên Ân 4 years 2021-08-14T18:34:19+00:00 1 Answers 27 views 0

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  1. ngochoa
    0
    2021-08-14T18:35:43+00:00
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    Answer:

    8

    Step-by-step explanation:

    Given the expression

    4t^6-r^10 we are to factorize in the form;

    (2t^x+r^y)(2t^x-r^y)

    First we need to factorize (2t^x+r^y)(2t^x-r^y)

    = (2t^x+r^y)(2t^x-r^y)\\= 4t^{2x}-2t^xr^y + 2t^xr^y - r^{2y}\\= 4t^{2x}-r^{2y}

    Compare 4t^{2x}-r^{2y} \ with \ 4t^6-r^{10}

    4t^{2x} = 4t^6\\t^{2x} = t^6\\equate \ the \ powers\\2x = 6\\x = 3\\

    Get y;

    r^{2y} = r^{10}\\2y = 10\\y = 5\\Hence \ x + y = 3+5 = 8

    Hence the sum of x and y is 8

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