Calculating the Degree of a Term

Oct 13, 2025 by windailys.com 49 views

When dealing with algebraic expressions, it's essential to understand the concept of degrees. The degree of a term is the sum of the exponents of its variables. In this article, we'll explore how to determine the degree of a term and apply this knowledge to select the correct answer from a given set of options.

What is the Degree of a Term?

The degree of a term is calculated by adding the exponents of its variables. For example, in the term $x^3y^2$ , the degree is $3 + 2 = 5$ . This means that the term $x^3y^2$ has a degree of 5.

Calculating the Degree of a Term

To calculate the degree of a term, follow these steps:

Identify the variables in the term.
Determine the exponent of each variable.
Add the exponents of the variables.

For example, consider the term $-2x^3y^5$ . To calculate its degree, follow these steps:

Identify the variables: $x$ and $y$ .
Determine the exponent of each variable: $x^3$ and $y^5$ .
Add the exponents: $3 + 5 = 8$ .

Therefore, the degree of the term $-2x^3y^5$ is 8.

Selecting the Correct Answer

Now that we understand how to calculate the degree of a term, let's apply this knowledge to select the correct answer from the given options.

Option A: $8xy$

To determine the degree of the term $8xy$ , we need to calculate the sum of the exponents of its variables. Since $x$ has an exponent of 1 and $y$ has an exponent of 1, the degree of the term $8xy$ is $1 + 1 = 2$ .

Option B: $-2x^3y^5$

As we calculated earlier, the degree of the term $-2x^3y^5$ is 8.

Option C: $3x^2y^4$

To determine the degree of the term $3x^2y^4$ , we need to calculate the sum of the exponents of its variables. Since $x$ has an exponent of 2 and $y$ has an exponent of 4, the degree of the term $3x^2y^4$ is $2 + 4 = 6$ .

Option D: $9xy^8$

To determine the degree of the term $9xy^8$ , we need to calculate the sum of the exponents of its variables. Since $x$ has an exponent of 1 and $y$ has an exponent of 8, the degree of the term $9xy^8$ is $1 + 8 = 9$ .

Conclusion

In conclusion, the correct answer is B. $-2x^3y^5$ , as it has a degree of 8. The other options have degrees of 2, 6, and 9, respectively.

Key Takeaways

The degree of a term is the sum of the exponents of its variables.
To calculate the degree of a term, identify the variables, determine their exponents, and add them together.
The degree of a term is essential in algebraic expressions, as it helps us understand the behavior of the expression.

Frequently Asked Questions

Q: What is the degree of a term? A: The degree of a term is the sum of the exponents of its variables.
Q: How do I calculate the degree of a term? A: Identify the variables, determine their exponents, and add them together.
Q: Why is the degree of a term important? A: The degree of a term helps us understand the behavior of the expression and is essential in algebraic expressions.
Frequently Asked Questions: Degrees of Terms in Algebra =====================================================

In our previous article, we explored the concept of degrees of terms in algebra. We discussed how to calculate the degree of a term and applied this knowledge to select the correct answer from a given set of options. In this article, we'll continue to answer some of the most frequently asked questions related to degrees of terms in algebra.

Q: What is the degree of a term?

A: The degree of a term is the sum of the exponents of its variables. For example, in the term $x^3y^2$ , the degree is $3 + 2 = 5$ . This means that the term $x^3y^2$ has a degree of 5.

Q: How do I calculate the degree of a term?

A: To calculate the degree of a term, follow these steps:

Identify the variables in the term.
Determine the exponent of each variable.
Add the exponents of the variables.

For example, consider the term $-2x^3y^5$ . To calculate its degree, follow these steps:

Identify the variables: $x$ and $y$ .
Determine the exponent of each variable: $x^3$ and $y^5$ .
Add the exponents: $3 + 5 = 8$ .

Therefore, the degree of the term $-2x^3y^5$ is 8.

Q: What is the difference between the degree of a term and the exponent of a variable?

A: The degree of a term is the sum of the exponents of its variables, while the exponent of a variable is the power to which the variable is raised. For example, in the term $x^3y^2$ , the exponent of $x$ is 3 and the exponent of $y$ is 2. The degree of the term is $3 + 2 = 5$ .

Q: Can a term have a negative degree?

A: No, a term cannot have a negative degree. The degree of a term is always a non-negative integer.

Q: How do I determine the degree of a term with multiple variables?

A: To determine the degree of a term with multiple variables, follow these steps:

Identify the variables in the term.
Determine the exponent of each variable.
Add the exponents of the variables.

For example, consider the term $x^3y^2z^4$ . To calculate its degree, follow these steps:

Identify the variables: $x$ , $y$ , and $z$ .
Determine the exponent of each variable: $x^3$ , $y^2$ , and $z^4$ .
Add the exponents: $3 + 2 + 4 = 9$ .

Therefore, the degree of the term $x^3y^2z^4$ is 9.

Q: Can a term have a degree of 0?

A: Yes, a term can have a degree of 0. For example, the term $x^0$ has a degree of 0, since the exponent of $x$ is 0.

Q: How do I use the degree of a term to simplify an expression?

A: To simplify an expression using the degree of a term, follow these steps:

Identify the terms in the expression.
Determine the degree of each term.
Combine like terms with the same degree.

For example, consider the expression $x^3 + 2x^3 + 3x^2$ . To simplify this expression, follow these steps:

Identify the terms: $x^3$ , $2x^3$ , and $3x^2$ .
Determine the degree of each term: $x^3$ has a degree of 3, $2x^3$ has a degree of 3, and $3x^2$ has a degree of 2.
Combine like terms with the same degree: $x^3 + 2x^3 = 3x^3$ and $3x^2$ remains the same.

Therefore, the simplified expression is $3x^3 + 3x^2$ .

Conclusion

In conclusion, the degree of a term is an essential concept in algebra that helps us understand the behavior of expressions. By calculating the degree of a term, we can simplify expressions and solve problems more efficiently. We hope that this article has helped you to better understand the concept of degrees of terms in algebra.