Final answer:
To find the product (bc)(x), multiply b(x) = -3x - 8 by c(x) = -3x + 8. The resulting polynomial in simplest form is 9x^2 - 64, as the middle terms cancel each other out.
Step-by-step explanation:
To find the product of the functions b(x) and c(x), denoted as (bc)(x), we need to multiply b(x) = -3x - 8 by c(x) = -3x + 8.
Here are the steps to perform this multiplication:
- First, we multiply -3x by -3x, which gives us 9x^2.
- Next, we multiply -3x by +8, which gives us -24x.
- Then, we multiply -8 by -3x, which also gives us +24x.
- Finally, we multiply -8 by +8, which gives us -64.
Adding up these results, we get:
9x^2 + (-24x) + 24x - 64
Notice how the -24x and +24x terms cancel each other out. Therefore, the final polynomial in simplest form is:
9x^2 - 64