Question

How do you multiply polynomials `[4 - (3c - 1)][6 - ( 3c - 1)]`?

Answer 1

`9c^2 - 36c + 35`

Explanation:

First of all, you can simplify both expressions inside the square bracket: for the first one, you get

`4-(3c-1)=4-3c-(-1)=4-3c+1=-3c+5`

In the same fashion, for the second square bracket you get

`6−(3c−1)=-3c+7`

Your multiplication is now written as

`(-3c+5)(-3c+7)`. To do such a multiplication, you need to do all the possible multiplications of the terms in the first bracket with those of the second, and them sum them up:

1. First term times first term: `(-3c)*(-3c)=9c^2`;
2. First term times second term: `(-3c)*7=-21c`;
3. Second term times first term: `5*(-3c)=-15c`
4. **Second term times second term: `5*7=35`.

Now we sum them up: `9c^2-21c-15c+35` equals

`9c^2 - 36c + 35`