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15 May, 00:05

From 6x2-7xy+8y2 subtract the sum of x2-3xy-y2 and 2x2+5xy-4y2

Every 2 is meant to be the power of 2

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  1. 15 May, 01:52
    0
    13 y^2 - 9 x y + 3 x^2

    Step-by-step explanation:

    Simplify the following:

    6 x^2 - 7 x y + 8 y^2 - (x^2 - 3 x y - y^2) - (2 x^2 + 5 x y - 4 y^2)

    - (x^2 - 3 x y - y^2) = - x^2 + 3 x y + y^2:

    6 x^2 - 7 x y + 8 y^2 + - x^2 + 3 x y + y^2 - (2 x^2 + 5 x y - 4 y^2)

    - (2 x^2 + 5 x y - 4 y^2) = - 2 x^2 - 5 x y + 4 y^2:

    6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 + - 2 x^2 - 5 x y + 4 y^2

    Grouping like terms, 6 x^2 - 7 x y + 8 y^2 - x^2 + 3 x y + y^2 - 2 x^2 - 5 x y + 4 y^2 = (8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2):

    (8 y^2 + y^2 + 4 y^2) + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)

    8 y^2 + y^2 + 4 y^2 = 13 y^2:

    13 y^2 + (-7 x y + 3 x y - 5 x y) + (6 x^2 - x^2 - 2 x^2)

    x y (-7) + x y 3 + x y (-5) = - 9 x y:

    13 y^2 + - 9 x y + (6 x^2 - x^2 - 2 x^2)

    6 x^2 - x^2 - 2 x^2 = 3 x^2:

    Answer: 13 y^2 - 9 x y + 3 x^2
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