Sure, let's go through this step by step.
1. Define the expressions with integers:
- Let’s choose [tex]\(a = 3\)[/tex], [tex]\(b = 4\)[/tex], and [tex]\(c = 2\)[/tex].
- Therefore, our expressions are [tex]\(3x\)[/tex] and [tex]\(4x + 2\)[/tex].
2. Form the expressions:
- The first expression is [tex]\(3x\)[/tex].
- The second expression is [tex]\(4x + 2\)[/tex].
3. Calculate the product of the two expressions:
- We need to multiply [tex]\(3x\)[/tex] by [tex]\(4x + 2\)[/tex].
- The product is given by:
[tex]\[
(3x) \cdot (4x + 2)
\][/tex]
4. Combine and simplify the expressions by multiplying:
- Distribute [tex]\(3x\)[/tex] over the terms inside the parentheses:
[tex]\[
3x \cdot 4x + 3x \cdot 2
\][/tex]
5. Simplify the product:
- [tex]\(3x \cdot 4x = 12x^2\)[/tex]
- [tex]\(3x \cdot 2 = 6x\)[/tex]
6. Combine the results:
- The product of the expressions is:
[tex]\[
12x^2 + 6x
\][/tex]
So, the product of the expressions [tex]\(3x\)[/tex] and [tex]\(4x + 2\)[/tex] is [tex]\(12x^2 + 6x\)[/tex].
