Question

How do you multiply `(t^2-3t+5)(t-1)`?

Answer 1

See the entire solution process below:

Explanation:

To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(t^2) - color(red)(3t) + color(red)(5))(color(blue)(t) - color(blue)(1))` becomes:

`(color(red)(t^2) xx color(blue)(t)) - (color(red)(t^2) xx color(blue)(1)) - (color(red)(3t) xx color(blue)(t)) + (color(red)(3t) xx color(blue)(1)) + (color(red)(5) xx color(blue)(t)) - (color(red)(5) xx color(blue)(1))`

`t^3 - t^2 - 3t^2 + 3t + 5t - 5`

We can now combine like terms:

`t^3 - (1 + 3)t^2 + (3 + 5)t - 5`

`t^3 - 4t^2 + 8t - 5`