To provide a detailed, step-by-step solution for the given expressions, let's break down the problem and identify each component.
### Given Expressions:
1. [tex]\( 3a \cdot x + 12a \)[/tex]
2. [tex]\( 2b \cdot x^2 + 6b \cdot x - 8b \)[/tex]
### Step-by-Step Breakdown:
#### Expression 1: [tex]\( 3a \cdot x + 12a \)[/tex]
- This is a linear expression in terms of [tex]\( x \)[/tex].
- The coefficient of [tex]\( x \)[/tex] is [tex]\( 3a \)[/tex].
- The constant term (the term independent of [tex]\( x \)[/tex]) is [tex]\( 12a \)[/tex].
- Therefore, the expression is simplified as:
[tex]\[
3a \cdot x + 12a
\][/tex]
#### Expression 2: [tex]\( 2b \cdot x^2 + 6b \cdot x - 8b \)[/tex]
- This is a quadratic expression in terms of [tex]\( x \)[/tex].
- The coefficient of the [tex]\( x^2 \)[/tex] term is [tex]\( 2b \)[/tex].
- The coefficient of the [tex]\( x \)[/tex] term is [tex]\( 6b \)[/tex].
- The constant term is [tex]\(-8b\)[/tex].
- Therefore, the expression is simplified as:
[tex]\[
2b \cdot x^2 + 6b \cdot x - 8b
\][/tex]
### Conclusion:
The two mathematical expressions are:
1. [tex]\( 3a \cdot x + 12a \)[/tex]
2. [tex]\( 2b \cdot x^2 + 6b \cdot x - 8b \)[/tex]
These are the simplified forms of the expressions involving coefficients [tex]\(a\)[/tex] and [tex]\(b\)[/tex], with terms in [tex]\(x\)[/tex] and constants respectively.
