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To solve this question, we need to determine how many terms are present in the given algebraic expression:

\[
-12 + 13ab + 23|x - y| + \sqrt{a^3} + b^3
\]

### Breakdown of terms:

1. **-12**: This is a constant term.
2. **13ab**: This is a product of constants and variables.
3. **23|x - y|**: This term involves the absolute value of \(x - y\), with a coefficient of 23.
4. **\(\sqrt{a^3}\)**: This is equivalent to \(a^{3/2}\), which is another term involving variables.
5. **\(b^3\)**: This is another term involving the variable \(b\).

Each part separated by a "+" or "-" sign is considered a separate term. Thus, there are **5 distinct terms** in the expression.

### Final Answer: 5 terms.

Would you like further details or have any questions?

Here are 5 related questions to explore further:
1. What is a term in an algebraic expression?
2. How do coefficients and variables combine in a term?
3. How are absolute value functions treated in algebraic expressions?
4. What are the rules for counting terms in a more complex expression?
5. How does exponentiation affect the classification of terms?

**Tip:** When counting terms in an expression, always check for individual segments separated by addition or subtraction signs.

How many terms are in the following algebraic expression: -12 + 13ab + 23|x - y| + √a^3 + b^3?

Learn how to count the terms in the algebraic expression -12 + 13ab + 23|x - y| + √a^3 + b^3. The expression includes constants, variables, absolute value, and square roots. Suitable for students in Grades 8-10.

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