Certainly! Let's multiply the two binomials [tex]\( (3x + 3)(2x + 9) \)[/tex] step by step to obtain the resulting trinomial.
### Step-by-Step Multiplication:
1. Set up the binomials for distribution:
[tex]\[
(3x + 3)(2x + 9)
\][/tex]
2. Distribute each term in the first binomial [tex]\( (3x + 3) \)[/tex] to each term in the second binomial [tex]\( (2x + 9) \)[/tex]:
- First, distribute [tex]\( 3x \)[/tex]:
[tex]\[
3x \cdot (2x + 9)
\][/tex]
- Multiply [tex]\( 3x \)[/tex] by [tex]\( 2x \)[/tex]:
[tex]\[
3x \cdot 2x = 6x^2
\][/tex]
- Multiply [tex]\( 3x \)[/tex] by [tex]\( 9 \)[/tex]:
[tex]\[
3x \cdot 9 = 27x
\][/tex]
- Second, distribute [tex]\( 3 \)[/tex]:
[tex]\[
3 \cdot (2x + 9)
\][/tex]
- Multiply [tex]\( 3 \)[/tex] by [tex]\( 2x \)[/tex]:
[tex]\[
3 \cdot 2x = 6x
\][/tex]
- Multiply [tex]\( 3 \)[/tex] by [tex]\( 9 \)[/tex]:
[tex]\[
3 \cdot 9 = 27
\][/tex]
3. Combine all the terms obtained:
- From distributing [tex]\( 3x \)[/tex]:
[tex]\[
6x^2 + 27x
\][/tex]
- From distributing [tex]\( 3 \)[/tex]:
[tex]\[
+ 6x + 27
\][/tex]
4. Combine like terms:
- Combine the [tex]\( x \)[/tex]-terms ([tex]\( 27x \)[/tex] and [tex]\( 6x \)[/tex]):
[tex]\[
6x^2 + 27x + 6x + 27 = 6x^2 + 33x + 27
\][/tex]
### Final Expanded Trinomial:
Thus, the expanded form of the expression [tex]\( (3x + 3)(2x + 9) \)[/tex] is:
[tex]\[
6x^2 + 33x + 27
\][/tex]
So, the resulting trinomial is:
[tex]\[
6x^2 + 33x + 27
\][/tex]
