To express [tex]\((3x + 1)(3x + 3)\)[/tex] as a trinomial, we can use the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last), to expand the product.
1. First Terms:
Multiply the first terms in each binomial:
[tex]\[
3x \cdot 3x = 9x^2
\][/tex]
2. Outer Terms:
Multiply the outer terms in the expression:
[tex]\[
3x \cdot 3 = 9x
\][/tex]
3. Inner Terms:
Multiply the inner terms in the expression:
[tex]\[
1 \cdot 3x = 3x
\][/tex]
4. Last Terms:
Multiply the last terms in each binomial:
[tex]\[
1 \cdot 3 = 3
\][/tex]
Next, we combine the results of these multiplications:
[tex]\[
(3x + 1)(3x + 3) = 9x^2 + 9x + 3x + 3
\][/tex]
Now, simplify by combining the like terms (the terms with [tex]\(x\)[/tex]):
[tex]\[
9x + 3x = 12x
\][/tex]
Thus, the trinomial expression is:
[tex]\[
9x^2 + 12x + 3
\][/tex]
Therefore, the final answer is:
[tex]\(\boxed{9x^2 + 12x + 3}\)[/tex]
