Question

How do you evaluate `(5a - 5) ( 9a ^ { 2} - 9a - 2)`?

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)(5a) - color(red)(5))(color(blue)(9a^2) - color(blue)(9a) - color(blue)(2))` becomes:

`(color(red)(5a) xx color(blue)(9a^2)) - (color(red)(5a) xx color(blue)(9a)) - (color(red)(5a) xx color(blue)(2)) - (color(red)(5) xx color(blue)(9a^2)) + (color(red)(5) xx color(blue)(9a)) + (color(red)(5) xx color(blue)(3))`

`45a^3 - 45a^2 - 10a - 45a^2 + 45a + 15`

We can now group and combine like terms:

`45a^3 - 45a^2 - 45a^2 - 10a + 45a + 15`

`45a^3 + (-45 - 45)a^2 + (-10 + 45)a + 15`

`45a^3 + (-90)a^2 + 35a + 15`

`45a^3 - 90a^2 + 35a + 15`