1.) 4(2-a)^2-81
2.) -(x-y)^3
3.)3x^2-27(2-x)^2
4.) 9(y-1)^2-25
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).