Question

How do you find the product `(9t+6)(9t-6)`?

Answer 1

See the solution process below:

Explanation:

This has a rule we can use to multiply the two terms:

`(a + b)(a - b) = a^2 - b^2`

Substituting 9t# for `a` and `6` for `b` gives:

`(9t + 6)(9t - 6) = (9t)^2 - 6^2 = 81t^2 - 36`

We can also use the long way to multiply these two terms and get the same result. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

`(color(red)(9t) + color(red)(6))(color(blue)(9t) - color(blue)(6))` becomes:

`(color(red)(9t) xx color(blue)(9t)) - (color(red)(9t) xx color(blue)(6)) + (color(red)(6) xx color(blue)(9t)) - (color(red)(6) xx color(blue)(6))`

`81t^2 - 54t + 54t - 36`

We can now combine like terms:

`81t^2 + (-54 + 54)t - 36`

`81t^2 + 0t - 36`

`81t^2 - 36`

Answer 2

`81t^2-36`

Explanation:

FOIL it! First, multiply `9t` by `9t`. Then multiply `9t` by `-6`. Then multiply `6` by `9t`. And lastly, multiply `6` by `-6`.

This is what it should look like:

`81t^2-54t+54t-36`

Which can then be simplified into:

`81t^2-36`