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Math help please

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1.) 4(2-a)^2-81

2.) -(x-y)^3

3.)3x^2-27(2-x)^2

4.) 9(y-1)^2-25

  • Math help please - ,

    1. 4(2-a)^2 - 81 , difference of squares
    = (2(2-a) + 9)(2(2-a) - 9)
    =(4 - 2a +9)(4 -2a - 9)
    = (-2a + 13)(-2a - 5)
    or
    (2a-13)(2a+5) , I wanted to start the brackets with a positive so I multiplies by (-1)(-1)

    Do #4 the same way.

    3.
    3x^2 - 27(2-x)^2
    = 3[x^2 - 9(2-x)} , again a difference of square
    = 3(x - 3(2-x))(x + 3(2-x))
    = 3(x - 6 + 3x)(x + 6 - 3x)
    = 3(4x-6)(6-2x)
    = 3(2)(2)(2x-3)(3-x)
    = 12(2x-3)(3-x)

    For #2,
    -(x-)(x-y)(x-y)
    = -(x-y)(x^2 - 2xy + y^2)
    = - (x^3 - 2x^2y + xy^2 - yx^2 + 2xy^2 - y^3)
    = - x^3 + 3yx^2 -3xy^2 + y^3

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