Question

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

2.) -(x-y)^3

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

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

Answer 1

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