Sure! Let's break this down step by step.
We need to multiply the two polynomials [tex]\((c + 3)\)[/tex] and [tex]\((3c + 1)\)[/tex]. Here’s how we can do it:
1. Distribute [tex]\(c\)[/tex] in the first polynomial over the second polynomial [tex]\((3c + 1)\)[/tex]:
[tex]\[
c \cdot (3c + 1)
\][/tex]
2. Distribute [tex]\(3\)[/tex] in the first polynomial over the second polynomial [tex]\((3c + 1)\)[/tex]:
[tex]\[
3 \cdot (3c + 1)
\][/tex]
Now let's perform the multiplication step by step:
3. Multiply [tex]\(c\)[/tex] by each term in the second polynomial:
[tex]\[
c \cdot 3c = 3c^2
\][/tex]
[tex]\[
c \cdot 1 = c
\][/tex]
4. Multiply [tex]\(3\)[/tex] by each term in the second polynomial:
[tex]\[
3 \cdot 3c = 9c
\][/tex]
[tex]\[
3 \cdot 1 = 3
\][/tex]
5. Combine all these results:
[tex]\[
3c^2 + c + 9c + 3
\][/tex]
6. Combine like terms ([tex]\(c\)[/tex] terms):
[tex]\[
c + 9c = 10c
\][/tex]
So, putting it all together, we get:
[tex]\[
3c^2 + 10c + 3
\][/tex]
Therefore, the simplified form of [tex]\((c + 3)(3c + 1)\)[/tex] is:
[tex]\[
3c^2 + 10c + 3
\][/tex]
