Select The Correct Answer.Which Choice Is A Term In This Expression? − 3 X − 7 ( X + 4 -3x - 7(x + 4 − 3 X − 7 ( X + 4 ]A. − 3 X -3x − 3 X B. X + 4 X + 4 X + 4 C. -3 D. -7

In algebra, an expression is a combination of variables, constants, and mathematical operations. When working with expressions, it's essential to understand the concept of terms. A term is a single part of an expression that can be added or subtracted. In this article, we'll explore how to identify terms in algebraic expressions.

What are Terms in Algebra?

A term in algebra is a single part of an expression that consists of a coefficient, a variable, or a constant. Terms are separated by addition or subtraction signs. For example, in the expression $2x + 3y - 4$, the terms are $2x$, $3y$, and $-4$.

Identifying Terms in Algebraic Expressions

To identify terms in an algebraic expression, follow these steps:

1. Look for addition or subtraction signs: Terms are separated by addition or subtraction signs. When you see an addition or subtraction sign, it indicates the start of a new term.
2. Identify the coefficient: A coefficient is a number that multiplies a variable. If a term has a coefficient, it's usually written in front of the variable.
3. Check for variables: Variables are letters or symbols that represent unknown values. If a term contains a variable, it's considered a term.
4. Look for constants: Constants are numbers that don't have variables. If a term contains a constant, it's considered a term.

Example 1: Identifying Terms in a Simple Expression

Consider the expression $x + 2y - 3$. To identify the terms, follow the steps above:

• Look for addition or subtraction signs: The expression contains addition and subtraction signs.
• Identify the coefficients: The coefficients are 1 (for $x$), 2 (for $2y$), and -3 (for $-3$).
• Check for variables: The expression contains the variables $x$ and $y$.
• Look for constants: The expression contains the constant $-3$.

The terms in the expression $x + 2y - 3$ are $x$, $2y$, and $-3$.

Example 2: Identifying Terms in a More Complex Expression

Consider the expression $-3x - 7(x + 4)$. To identify the terms, follow the steps above:

• Look for addition or subtraction signs: The expression contains addition and subtraction signs.
• Identify the coefficients: The coefficients are -3 (for $-3x$), -7 (for $-7(x + 4)$), and 1 (for $x$ and $4$ in the expression $x + 4$).
• Check for variables: The expression contains the variables $x$.
• Look for constants: The expression contains the constant $-7$ and $4$.

The terms in the expression $-3x - 7(x + 4)$ are $-3x$, $-7x$, $-7(4)$, and $-7(-4)$.

Answer to the Original Question

In the expression $-3x - 7(x + 4)$, the correct answer is B. $x + 4$. This is because $x + 4$ is a term in the expression, while $-3x$ and $-7$ are not terms in the expression $x + 4$.

Conclusion

In the previous article, we explored the concept of terms in algebraic expressions and how to identify them. However, we know that practice makes perfect, and there's no better way to practice than by answering questions. In this article, we'll provide a Q&A section to help you reinforce your understanding of identifying terms in algebraic expressions.

Q1: What is a term in an algebraic expression?

A term in an algebraic expression is a single part of the expression that can be added or subtracted. It consists of a coefficient, a variable, or a constant.

Q2: How do I identify terms in an algebraic expression?

To identify terms in an algebraic expression, follow these steps:

1. Look for addition or subtraction signs.
2. Identify the coefficient.
3. Check for variables.
4. Look for constants.

Q3: What is the difference between a term and an expression?

A term is a single part of an expression, while an expression is a combination of terms. For example, in the expression $2x + 3y - 4$, the terms are $2x$, $3y$, and $-4$.

Q4: Can a term have more than one variable?

Yes, a term can have more than one variable. For example, in the expression $2xy + 3x$, the term $2xy$ has two variables, $x$ and $y$.

Q5: Can a term have a negative coefficient?

Yes, a term can have a negative coefficient. For example, in the expression $-3x + 2y$, the term $-3x$ has a negative coefficient.

Q6: Can a term have a coefficient of 1?

Yes, a term can have a coefficient of 1. For example, in the expression $x + 2y - 3$, the term $x$ has a coefficient of 1.

Q7: Can a term have a variable with an exponent?

Yes, a term can have a variable with an exponent. For example, in the expression $2x^2 + 3y$, the term $2x^2$ has a variable with an exponent.

Q8: Can a term have a constant with a negative sign?

Yes, a term can have a constant with a negative sign. For example, in the expression $-3x + 2y - 4$, the term $-4$ has a negative sign.

Q9: How do I identify terms in a complex expression?

To identify terms in a complex expression, follow the same steps as before:

1. Look for addition or subtraction signs.
2. Identify the coefficient.
3. Check for variables.
4. Look for constants.

Q10: Can I have multiple terms with the same variable?

Yes, you can have multiple terms with the same variable. For example, in the expression $2x + 3x - 4$, the terms $2x$ and $3x$ both have the variable $x$.

Answer Key

Here are the answers to the questions above:

1. A term in an algebraic expression is a single part of the expression that can be added or subtracted.
2. To identify terms in an algebraic expression, follow these steps: Look for addition or subtraction signs, identify the coefficient, check for variables, and look for constants.
3. A term is a single part of an expression, while an expression is a combination of terms.
4. Yes, a term can have more than one variable.
5. Yes, a term can have a negative coefficient.
6. Yes, a term can have a coefficient of 1.
7. Yes, a term can have a variable with an exponent.
8. Yes, a term can have a constant with a negative sign.
9. To identify terms in a complex expression, follow the same steps as before: Look for addition or subtraction signs, identify the coefficient, check for variables, and look for constants.
10. Yes, you can have multiple terms with the same variable.

Conclusion

Identifying terms in algebraic expressions is a crucial skill for solving equations and manipulating expressions. By following the steps outlined in this article and practicing with the Q&A section, you'll become more confident in your ability to identify terms in algebraic expressions. Remember to look for addition or subtraction signs, identify coefficients, check for variables, and look for constants to identify terms in expressions.