Question

How do you find the product `(3a^4-b)(3a^4+b)`?

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)(3a^4) - color(red)(b))(color(blue)(3a^4) + color(blue)(b))` becomes:

`(color(red)(3a^4) xx color(blue)(3a^4)) + (color(red)(3a^4) xx color(blue)(b)) - (color(red)(b) xx color(blue)(3a^4)) - (color(red)(b) xx color(blue)(b))`

`9a^8 + 3a^4b - 3a^4b - b^2`

We can now combine like terms:

`9a^8 + (3 - 3)a^4b - b^2`

`9a^8 + 0a^4b - b^2`

`9a^8 - b^2`