Consider The Following Expression: $ 9b + 4 + 5a\$} .Select All Of The True Statements Below A. 5 Is A Coefficient.B. ${$5a$ $ And 4 Are Like Terms.C. ${ 9b + 4 + 5a\$} Is Written As A Sum Of Three Terms.D. 4 Is A Constant.E.
In algebra, expressions are a combination of variables, constants, and mathematical operations. Understanding the components of an algebraic expression is crucial for simplifying, solving, and manipulating equations. In this article, we will delve into the world of algebraic expressions, focusing on coefficients, like terms, and constants. We will examine the given expression $<span class="katex-error" title="ParseError' at position 14: 9b + 4 + 5a$}̲" style="color:#cc0000">9b + 4 + 5a$} and determine which of the provided statements are true.
Coefficients: The Multiplicative Factors
A coefficient is a multiplicative factor in an algebraic expression. It is a number that is multiplied by a variable or a group of variables. In the expression ${9b + 4 + 5a\$}, the numbers 9 and 5 are coefficients because they are multiplied by the variables b and a, respectively.
- A. 5 is a coefficient. This statement is true. The number 5 is indeed a coefficient in the expression ${9b + 4 + 5a\$} because it is multiplied by the variable a.
Like Terms: The Similar Components
Like terms are algebraic expressions that have the same variable(s) raised to the same power. In the expression ${9b + 4 + 5a\$}, the terms ${5a\$} and 4 are not like terms because they do not have the same variable(s) raised to the same power. However, the terms ${9b\$} and 4 are not like terms either because they do not have the same variable(s) raised to the same power.
- B. ${5a\$} and 4 are like terms. This statement is false. The terms ${5a\$} and 4 are not like terms because they do not have the same variable(s) raised to the same power.
Constants: The Non-Variant Components
A constant is a number that is not a variable. In the expression ${9b + 4 + 5a\$}, the number 4 is a constant because it is not a variable.
- D. 4 is a constant. This statement is true. The number 4 is indeed a constant in the expression ${9b + 4 + 5a\$} because it is not a variable.
The Sum of Terms: A Closer Look
An algebraic expression can be written as a sum of terms. In the expression $9b + 4 + 5a\$}, the expression is written as a sum of three terms$, 4, and ${5a\$}.
- **C. $9b + 4 + 5a\$} is written as a sum of three terms.** This statement is true. The expression ${9b + 4 + 5a\$} is indeed written as a sum of three terms$, 4, and ${5a\$}.
Conclusion
In conclusion, understanding the components of an algebraic expression is crucial for simplifying, solving, and manipulating equations. Coefficients, like terms, and constants are essential components of an algebraic expression. By examining the given expression ${9b + 4 + 5a\$}, we have determined which of the provided statements are true. The statements A, C, and D are true, while statement B is false.
Key Takeaways
- Coefficients are multiplicative factors in an algebraic expression.
- Like terms are algebraic expressions that have the same variable(s) raised to the same power.
- Constants are numbers that are not variables.
- An algebraic expression can be written as a sum of terms.
Further Reading
- Algebraic Expressions: A Comprehensive Guide
- Simplifying Algebraic Expressions: A Step-by-Step Approach
- Manipulating Algebraic Expressions: A Guide to Equations and Inequalities
Frequently Asked Questions: Algebraic Expressions =====================================================
In our previous article, we explored the world of algebraic expressions, focusing on coefficients, like terms, and constants. We examined the expression ${9b + 4 + 5a\$} and determined which of the provided statements were true. In this article, we will answer some frequently asked questions about algebraic expressions.
Q: What is an algebraic expression?
A: An algebraic expression is a combination of variables, constants, and mathematical operations. It is a way to represent a value or a relationship between values using variables, numbers, and mathematical operations.
Q: What is a coefficient?
A: A coefficient is a multiplicative factor in an algebraic expression. It is a number that is multiplied by a variable or a group of variables.
Q: What are like terms?
A: Like terms are algebraic expressions that have the same variable(s) raised to the same power. They can be added or subtracted from each other.
Q: What is a constant?
A: A constant is a number that is not a variable. It is a value that does not change.
Q: How do I simplify an algebraic expression?
A: To simplify an algebraic expression, you need to combine like terms and eliminate any unnecessary parentheses or brackets.
Q: What is the order of operations?
A: The order of operations is a set of rules that tells you which operations to perform first when simplifying an algebraic expression. The order of operations is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I write an algebraic expression as a sum of terms?
A: To write an algebraic expression as a sum of terms, you need to identify the individual terms and combine them using addition or subtraction.
Q: What is the difference between an algebraic expression and an equation?
A: An algebraic expression is a combination of variables, constants, and mathematical operations, while an equation is a statement that says two expressions are equal.
Q: How do I solve an equation?
A: To solve an equation, you need to isolate the variable by performing inverse operations to both sides of the equation.
Conclusion
In conclusion, algebraic expressions are a fundamental concept in mathematics, and understanding them is crucial for solving equations and manipulating algebraic expressions. By answering these frequently asked questions, we hope to have provided a better understanding of algebraic expressions and their components.
Key Takeaways
- Algebraic expressions are a combination of variables, constants, and mathematical operations.
- Coefficients are multiplicative factors in an algebraic expression.
- Like terms are algebraic expressions that have the same variable(s) raised to the same power.
- Constants are numbers that are not variables.
- The order of operations is a set of rules that tells you which operations to perform first when simplifying an algebraic expression.
Further Reading
- Algebraic Expressions: A Comprehensive Guide
- Simplifying Algebraic Expressions: A Step-by-Step Approach
- Manipulating Algebraic Expressions: A Guide to Equations and Inequalities