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12 June, 09:55

X (x-2) - y (y-2)

Factorize clearly with all steps.

Best answer gets marked brainliest.

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Answers (1)
  1. 12 June, 11:28
    0
    (x - y) (y + x - 2)

    Step-by-step explanation:

    Factor the following:

    x (x - 2) - y (y - 2)

    x (x - 2) = x^2 - 2 x:

    x^2 - 2 x - y (y - 2)

    -y (y - 2) = 2 y - y^2:

    -2 x + x^2 + 2 y - y^2

    -2 x + x^2 + 2 y - y^2 = (x - 1) ^2 - (y - 1) ^2:

    (x - 1) ^2 - (y - 1) ^2

    Factor the difference of two squares. (x - 1) ^2 - (y - 1) ^2 = ((x - 1) - (y - 1)) ((x - 1) + (y - 1)):

    (-1 + x - (y - 1)) (-1 + x - 1 + y)

    Grouping like terms, - 1 + x - 1 + y = y + x + (-1 - 1):

    y + x + (-1 - 1) (-1 + x - (y - 1))

    -1 - 1 = - 2:

    (-1 + x - (y - 1)) (y + x + - 2)

    - (y - 1) = 1 - y:

    (-1 + x + 1 - y) (y + x - 2)

    Grouping like terms, - 1 + x + 1 - y = - y + x + (1 - 1):

    -y + x + (1 - 1) (y + x - 2)

    1 - 1 = 0:

    Answer: (x - y) (y + x - 2)
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