Question

How do you evaluate `(5y - 7) ( 5y ^ { 2} - y - 1)`?

Answer 1

As no identities apply on this, you have to do it by distributive property
`5y(5y^2-y-1) - 7(5y^2-y-1)`
`[25y^3-5y^2-5y]-[35y^2-7y-7]`
`25y^3-5y^2-5y-35y^2+7y+7`
Regroup
`25y^3-5y^2-35y^2-5y+7y+7`
You get
`25y^3-40y^2+2y+7`

Answer 2

`color(white)color(green)(25y^3-40y^2+2y+7)`

Explanation:

`(5y-7)(5y^2-y-1)`

`color(white)(aaaaaaaaaaaaa)` `5y^2-y-1`
`color(white)(aaaaaaaaaaa)` `xx underline(5y-7)`
`color(white)(aaaaaaaaaaaaa)` `25y^3-5y^2-5y`
`color(white)(aaaaaaaaaaaaaaaaa)` `-35y^2+7y+7`
`color(white)(aaaaaaaaaaaaa)` `overline(25y^3-40y^2+2y+7)`

`color(white)(aaaaaaaaaaaaa)` `color(green)(25y^3-40y^2+2y+7)`