Question

How do you multiply `(x-7)(5x^2-3x-5)`?

Answer 1

`5x^3-38x^2+16x+35`

Explanation:

`"each term in the second bracket is multiplied by each "`
`"term in the first bracket, as follows."`

`(color(red)(x-7))(5x^2-3x-5)`

`=color(red)(x)(5x^2-3x-5)color(red)(-7)(5x^2-3x-5)`

`"distributing each bracket gives"`

`=5x^3-3x^2-5x-35x^2+21x+35`

`"collect like terms for simplification"`

`=5x^3-38x^2+16x+35`

Answer 2

`color(green)(5x^3-38x^2+16x+35`

Explanation:

`(x-7)(5x^2-3x-5)`

`:.x xx 5x^2=5x^3`

`:.x xx -3x=-3x^2`

`:.x xx -5=-5x`

`:.-7 xx 5x^2=-35x^2`

`:.-7 xx -3x=21x`

`:.-7 xx -5=35`

`:.=5x^3-3x^2-35x^2-5x+21x+35`

`:.color(green)(=5x^3-38x^2+16x+35`

or:-

`color(white)(aaaaaaaaaaaaa)` `5x^2-3x-5`
`color(white)(aaaaaaaaaaa)` `xx underline(x-7)`
`color(white)(aaaaaaaaaaaaa)` `5x^3-3x^2-5x`
`color(white)(aaaaaaaaaaaaaaaa)` `-35x^2+21x+35`
`color(white)(aaaaaaaaaaaaa)` `overline(5x^3-38x^2+16x+35)`

`color(white)(aaaaaaaaaaaaa)` `color(green)(5x^3-38x^2+16x+35`