Certainly! Let's go through the process step-by-step to understand how the given expression [tex]\(6ab^2 - 3b + 2\)[/tex] is formed in a detailed manner:
### Understanding Variables and Constants
1. Variables: The expression includes two variables, [tex]\(a\)[/tex] and [tex]\(b\)[/tex], which can represent any real numbers.
2. Constants: The numbers 6, -3, and 2 are constants in this expression.
### Forming the Expression
The expression [tex]\(6ab^2 - 3b + 2\)[/tex] consists of three distinct terms:
1. First Term: [tex]\(6ab^2\)[/tex]
- This term is a product of three factors: the constant 6, the variable [tex]\(a\)[/tex], and the square of the variable [tex]\(b\)[/tex] ([tex]\(b^2\)[/tex]).
- Here, [tex]\(b^2\)[/tex] means [tex]\(b\)[/tex] multiplied by itself.
- When you multiply 6, [tex]\(a\)[/tex], and [tex]\(b^2\)[/tex] together, it forms the term [tex]\(6ab^2\)[/tex].
2. Second Term: [tex]\(-3b\)[/tex]
- This term is formed by multiplying the constant -3 with the variable [tex]\(b\)[/tex].
- The negative sign indicates that this term subtracts from the overall expression.
3. Third Term: [tex]\(2\)[/tex]
- This is a constant term with no variables, so it remains 2 throughout the expression.
### Combining the Terms
To create the final expression:
1. Start with the first term: [tex]\(6ab^2\)[/tex].
2. Subtract the second term: [tex]\(-3b\)[/tex].
3. Finally, add the third term: [tex]\(2\)[/tex].
Therefore, combining these steps, we get:
[tex]\[
6ab^2 - 3b + 2
\][/tex]
This expression shows a combination of multiplication, subtraction, and addition involving variables [tex]\(a\)[/tex] and [tex]\(b\)[/tex], as well as constants.
### Final Expression
[tex]\[
\boxed{6ab^2 - 3b + 2}
\][/tex]
This concludes our step-by-step breakdown of the given mathematical expression.
