After simplification, how many terms will there be in [tex]$4 x^3+9 y^2-3 x+2-1$[/tex]?
Answer (2)
Simplify the expression by combining the constant terms: 2 − 1 = 1 .
Identify the terms in the simplified expression: 4 x 3 , 9 y 2 , − 3 x , and 1 .
Count the number of terms: There are 4 terms.
The number of terms after simplification is 4 .
Explanation
Simplifying the Expression We are given the expression 4 x 3 + 9 y 2 − 3 x + 2 − 1 and asked to find the number of terms after simplification. First, we simplify the constant terms: 2 − 1 = 1 . So the simplified expression is 4 x 3 + 9 y 2 − 3 x + 1 .
Counting the Terms Now, we count the number of terms in the simplified expression 4 x 3 + 9 y 2 − 3 x + 1 . The terms are 4 x 3 , 9 y 2 , − 3 x , and 1 . There are 4 terms in total.
Final Answer Therefore, after simplification, there are 4 terms in the expression.
Examples
In algebra, identifying the number of terms in an expression is crucial for understanding its structure and complexity. For instance, when analyzing polynomial functions, the number of terms can indicate the potential number of turning points or the degree of the polynomial. This skill is also useful in simplifying complex equations in physics or engineering, where each term might represent a different physical quantity or effect. By recognizing and counting terms, students can better manipulate and interpret mathematical models in various real-world applications.
After simplifying the expression 4 x 3 + 9 y 2 − 3 x + 2 − 1 , there are 4 terms in total. The expression simplifies to 4 x 3 + 9 y 2 − 3 x + 1 . Hence, the final count of terms is 4.
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