Question

PLSSS ANSWER, 35 pointss

Write as a product of two polynomials.

1. x(y–5)–y(5–y)
2. (x–y)^2–a(y–x)
3. 2(3–b)+5(b–3)^2

Answer 1

1.

`(y - 5)(x + y)`

2.

`{(x - y)}(x - y + a)`

3.

`(b - 3)(5b - 17)`

Explanation:

1. The given polynomial is

`x(y - 5) - y(5 - y)`

We need to factor the second part to get:

`x(y - 5) + y(y - 5)`

We factor y-5 to obtain:

`(y - 5)(x + y)`

2. We have

`{(x - y)}^(2) - a(y - x)`

We again factor -1 from the second part to get:

`{(x - y)}^(2) + a(x- y)`

We now factor x-y to get:

`{(x - y)}^(2) + a(x- y)`

`{(x - y)}(x - y + a)`

3. We have

`2(3 - b) + 5 {(b - 3})^(2)`

We factor negative 1 from the first part to get

`- 2(b - 3) + 5 {(b - 3})^(2)`

We now factor b-3 to get:

`(b - 3)( - 2 + 5(b - 3))`

We now simplify to get:

`(b - 3)( - 2 + 5b - 15) = (b - 3)(5b - 17)`