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

1 Answer
Oct 15, 2015

Answer:

#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#