Question

How do you multiply `(4m - 6) ( - 6m + 3)`?

Answer 1

`-24m^2+48m-18`

Explanation:

`"each term in the second factor is multiplied by each term"`
`"in the first factor"`

`(color(red)(4m-6))(-6m+3)`

`=color(red)(4m)(-6m+3)color(red)(-6)(-6m+3)larrcolor(blue)"distribute"`

`=(color(red)(4m)xx-6m)+(color(red)(4m)xx3)+(color(red)(-6)xx-6m)+(color(red)(-6)xx3)`

`=-24m^2color(blue)(+12m)color(blue)(+36m)-18larrcolor(magenta)"collect like terms"`

`=-24m^2+48m-18`

Answer 2

`color(green)(-24m^2+42m-18`

Explanation:

`(4m-6)(-6m+3)`

`color(white)(aaaaaaaaaaaaaaa)` `4m-6`
`color(white)(aaaaaaaaaaa)` `xx underline(-6m+3)`
`color(white)(aaaaaaaaaaaaa)` `-24m^2+36m`
`color(white)(aaaaaaaaaaaaaaaaaaaa)` `+12m-18`
`color(white)(aaaaaaaaaaaaa)` `overline(-24m^2+42m-18)`

`color(white)(aaaaaaaaaaaaa)` `color(green)(-24m^2+42m-18`