Question

How do you find the product `(8a^2-9b^3)(8a^2+9b^3)`?

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)(8a^2) - color(red)(9b^3))(color(blue)(8a^2) + color(blue)(9b^3))` becomes:

`(color(red)(8a^2) xx color(blue)(8a^2)) + (color(red)(8a^2) xx color(blue)(9b^3)) - (color(red)(9b^3) xx color(blue)(8a^2)) - (color(red)(9b^3) xx color(blue)(9b^3))`

`64a^4 + 72a^2b^3 - 72a^2b^3 - 81b^6`

We can now combine like terms:

`64a^4 + (72 - 72)a^2b^3 - 81b^6`

`64a^4 + 0a^2b^3 - 81b^6`

`64a^4 - 81b^6`