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Math

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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 - ,

    1. 4(2-a)^2 -81 =
    4(4-4a+a^2) -81 =
    4a^2 - 16a + 16 -81 =
    4a^2 - 16a - 65 =

    2. -(x-y)^3 =
    -(x-y)^2(x-y) =
    -(x^2-2xy+y^2)(x-y) =
    -(x^3-x^2y-2x^2y-2xy^2+xy^2-y^3) =
    Combine like-terms:
    -(x^3-3x^2y-xy^2-y^3) =
    -x^3 + 3x^2y + xy^2 + y^3.

    3. 3x^2 -27(2-x)^2 =
    3x^2-27(4-4x+x^2) =
    3(x^2-9)(x^2-4x+4) =
    3(x+3)(x-3)(x-2)(x-2).

    4. 9(y-1)^2-25 =
    The difference of 2 squares:
    (3(y-1)+5)(3(y-1)-5)) =
    (3y-3+5)(3y-3-5) =
    (3y+2)(3y-8).

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