Question

How do you multiply `(3b + 4) ( - b ^ { 2} + 3b - 4)`?

Answer 1

Distribute the `3b` among the `(-b^2+3b-4)`

To get

`-3b^3+9b^2-12b`

Then distribute the `+4` among the `(-b^2+3b-4)`

To get

`-4b^2+12b-16`

Then combine the two equations you formed like so:

`-3b^3+9b^2-12b-4b^2+12b-16`

Simplify to get the answer:

`-3b^3+5b^2-16`

Answer 2

`-3b^3+5b^2-16`

Explanation:

Each term in the second bracket is multiplied by each term in the first bracket as shown below.

`(color(red)(3b+4))(-b^2+3b-4)`

`=color(red)(3b)(-b^2+3b-4)color(red)(+4)(-b^2+3b-4)`

`=(color(red)(3b)xx-b^2)+(color(red)(3b)xx3b)+(color(red)(3b)xx-4)`
`color(white)(=)+(color(red)(4)xx-b^2)+(color(red)(4)xx3b)+(color(red)(4)xx-4)`

`=-3b^3+9b^2cancel(-12b)-4b^2cancel(+12b)-16`

`=-3b^3+5b^2-16`