Question

How do you simplify `(-8p+5)(-5p^2+4p-7)`?

Answer 1

See a 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)(-8p) + color(red)(5))(color(blue)(-5p^2) + color(blue)(4p) - color(blue)(7))` becomes:

`(color(red)(8p) xx color(blue)(5p^2)) - (color(red)(8p) xx color(blue)(4p)) + (color(red)(8p) xx color(blue)(7)) - (color(red)(5) xx color(blue)(5p^2)) + (color(red)(5) xx color(blue)(4p)) - (color(red)(5) xx color(blue)(7))`

`40p^3 - 32p^2 + 56p - 25p^2 + 20p - 35`

We can now group and combine like terms:

`40p^3 - 32p^2 - 25p^2 + 56p + 20p - 35`

`40p^3 + (-32 - 25)p^2 + (56 + 20)p - 35`

`40p^3 + (-57)p^2 + 76p - 35`

`40p^3 - 57p^2 + 76p - 35`