Simplifying Expressions Worksheet

Oct 13, 2025 by leolavanderia.com.br 2 views

Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently. It involves combining like terms, removing unnecessary brackets, and rearranging the terms to make the expression more manageable. In this article, we will simplify the given expression: $(6 + 2x) + 3$ . We will break down the steps involved in simplifying the expression and provide a clear explanation of each step.

Understanding the Expression

The given expression is $(6 + 2x) + 3$ . To simplify this expression, we need to understand the order of operations (PEMDAS) and the concept of like terms. The expression consists of two terms: $6 + 2x$ and $3$ . We can simplify the expression by combining these two terms.

Combining Like Terms

Like terms are terms that have the same variable raised to the same power. In this case, we have two terms: $6 + 2x$ and $3$ . The term $6$ does not have any variable, while the term $2x$ has a variable $x$ . We can combine these two terms by adding their coefficients.

Simplifying the Expression

To simplify the expression, we need to combine the two terms: $6 + 2x$ and $3$ . We can do this by adding their coefficients. The coefficient of the term $6$ is $1$ , and the coefficient of the term $2x$ is $2$ . We can add these coefficients to get the simplified expression.

Step-by-Step Solution

Here's a step-by-step solution to simplify the expression:

Combine the constants: The constant term in the expression is $6$ . We can combine this term with the constant term $3$ by adding them.
Combine the variables: The variable term in the expression is $2x$ . We can combine this term with the variable term $0x$ (which is implied by the constant term $3$ ) by adding their coefficients.
Simplify the expression: After combining the constants and variables, we get the simplified expression.

Simplified Expression

Let's simplify the expression step by step:

Combine the constants: $6 + 3 = 9$
Combine the variables: $2x + 0x = 2x$
Simplify the expression: $(6 + 2x) + 3 = 9 + 2x$

Conclusion

In this article, we simplified the expression $(6 + 2x) + 3$ by combining like terms and removing unnecessary brackets. We followed the order of operations (PEMDAS) and used the concept of like terms to simplify the expression. The simplified expression is $9 + 2x$ . We hope this article has provided a clear explanation of how to simplify expressions in mathematics.

Frequently Asked Questions

What is the order of operations (PEMDAS)? The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
What are like terms? Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $4x$ are like terms because they both have the variable $x$ raised to the power of $1$ .
How do I simplify an expression? To simplify an expression, you need to combine like terms, remove unnecessary brackets, and rearrange the terms to make the expression more manageable. You can use the order of operations (PEMDAS) to determine which operations to perform first.

Introduction

In our previous article, we simplified the expression $(6 + 2x) + 3$ by combining like terms and removing unnecessary brackets. We hope this article has provided a clear explanation of how to simplify expressions in mathematics. In this Q&A article, we will answer some frequently asked questions about simplifying expressions.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, $2x$ and $4x$ are like terms because they both have the variable $x$ raised to the power of $1$ .

Q: How do I simplify an expression?

A: To simplify an expression, you need to combine like terms, remove unnecessary brackets, and rearrange the terms to make the expression more manageable. You can use the order of operations (PEMDAS) to determine which operations to perform first.

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change. For example, $x$ is a variable. A constant is a value that does not change. For example, $3$ is a constant.

Q: How do I combine like terms?

A: To combine like terms, you need to add or subtract the coefficients of the terms. For example, if you have the expression $2x + 4x$ , you can combine the terms by adding their coefficients: $2x + 4x = 6x$ .

Q: What is the distributive property?

A: The distributive property is a rule that allows us to multiply a single term by multiple terms. For example, if you have the expression $2(x + 3)$ , you can use the distributive property to multiply the term $2$ by each term inside the parentheses: $2(x + 3) = 2x + 6$ .

Q: How do I simplify an expression with parentheses?

A: To simplify an expression with parentheses, you need to follow the order of operations (PEMDAS). First, evaluate any expressions inside the parentheses. Then, simplify the expression by combining like terms and removing unnecessary brackets.

Q: What is the difference between a linear expression and a quadratic expression?

A: A linear expression is an expression that has a single variable raised to the power of $1$ . For example, $2x$ is a linear expression. A quadratic expression is an expression that has a single variable raised to the power of $2$ . For example, $x^2$ is a quadratic expression.

Q: How do I simplify an expression with exponents?

A: To simplify an expression with exponents, you need to follow the order of operations (PEMDAS). First, evaluate any expressions with exponents. Then, simplify the expression by combining like terms and removing unnecessary brackets.

Conclusion

In this Q&A article, we have answered some frequently asked questions about simplifying expressions. We hope this article has provided a clear explanation of how to simplify expressions in mathematics. If you have any more questions, feel free to ask!

Additional Resources

Simplifying Expressions Worksheet: This worksheet provides practice exercises on simplifying expressions.
Simplifying Expressions Video: This video provides a step-by-step guide on simplifying expressions.
Simplifying Expressions Online Quiz: This online quiz tests your knowledge on simplifying expressions.