Question

How do you find the product `[(t^2+3t-8)-(t^2-2t+6)](t-4)`?

Answer 1

`[(t^2+3t-8)-(t^2-2t+6)] (t-4) = 5t^2-34t+56`

Explanation:

`[(cancel(t^2)+3t-8)-(cancel(t^2)-2t+6)] (t-4)`

`= (5t-14)(t-4)`

We have the first term:
`t^2+3t-8-t^2+2t+6=5t-14`
so we get
`[(cancel(t^2)+3t-8)-(cancel(t^2)-2t+6)] (t-4)`

`= (5t-14)(t-4)`

`(5t-14)(t-4)=5t^2-14t-20t+56`
Combining like terms, we get:
`5t^2-34t+56`