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# Combining Like Terms and Distributive Property

Welcome to the exciting world of combining like terms and the distributive property, where Grade 7 students will discover the tools to simplify and manipulate algebraic expressions. In this article, we delve into the fundamental concepts that form the backbone of algebraic operations.

By understanding how to combine like terms and apply the distributive property, students unlock the ability to simplify complex expressions and solve equations more efficiently. Through engaging examples and step-by-step explanations, we explore the techniques and strategies necessary to master these concepts.

• Combining Like Terms
• Distributive Property
• Solved Examples
• Real-life Applications
• FAQs

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## Combining Like Terms:

Terms are terms that have the same variable raised to the same exponent. Combining like terms involves adding or subtracting the coefficients of these terms while keeping the variables unchanged.

By combining like terms, expressions are simplified and condensed. It is important to identify like terms by their variables and exponents before performing the necessary operations. The general formula for combining like terms is:

Like Terms Combined = Coefficient₁ * Variable₁ + Coefficient₂ * Variable₁ + … ## Distributive Property:

The distributive property allows us to multiply a term by each term inside parentheses. This property helps simplify expressions by distributing the multiplication. It is particularly useful when dealing with expressions involving multiplication or when simplifying equations with multiple terms.

The general formula for the distributive property is:

a * (b + c) = a * b + a * c

## Simplification of Complex Expressions:

Combining like terms and utilizing the distributive property are often combined to simplify complex expressions. By applying these techniques repeatedly, expressions can be condensed into a more manageable and concise form. This simplification allows for easier analysis, manipulation, and solving of equations.

## Solved Examples

Example 1: Combining Like Terms
Simplify the expression: 3x + 2y – 5x + 4y

Solution:
To combine like terms, add the coefficients of x and y:
(3x – 5x) + (2y + 4y) = -2x + 6y

The simplified expression is -2x + 6y.

Example 2: Distributive Property
Simplify the expression: 2(3x – 5)

Solution:
Using the distributive property, multiply 2 by each term inside the parentheses:
2 * 3x – 2 * 5 = 6x – 10

The simplified expression is 6x – 10.

Example 3: Simplification of Complex Expressions
Simplify the expression: 2(3x + 4) – 3(2x – 1)

Solution:
Using the distributive property and combining like terms:
2 * 3x + 2 * 4 – 3 * 2x + 3 * 1 = 6x + 8 – 6x + 3 = 11

The simplified expression is 11.
Example 4: Simplifying Equations
Simplify the equation: 2(x + 3) – 4x = 10 – x

Solution:
Using the distributive property and combining like terms:
2x + 6 – 4x = 10 – x
-2x + 6 = 10 – x

Next, isolate the variable:
-2x + x = 10 – 6
-x = 4
x = -4

The solution to the equation is x = -4.

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## Real-life Applications

Finance and Budgeting:
Combining like terms and distributive property is used in financial calculations, such as budgeting and expense tracking. By simplifying and organizing financial equations, individuals can effectively manage their income, expenses, and savings.

Algebraic Modeling in Science and Engineering:
The principles of combining like terms and the distributive property are essential in algebraic modeling for scientific and engineering calculations. They help simplify complex equations and expressions, enabling scientists and engineers to analyze data, make predictions, and solve real-world problems.

Architecture and Construction:
Architects and construction professionals use algebraic techniques, including combining like terms and the distributive property, to simplify calculations related to measurements, quantities, and materials. This allows for accurate estimations and cost analysis in designing and constructing buildings.

Combining like terms and distributive property plays a crucial role in business and economic analysis. They are used to simplify mathematical models, evaluate profit and loss scenarios, calculate expenses, and optimize production and sales strategies.

Data Analysis and Statistics:
In data analysis and statistics, simplifying expressions using the distributive property and combining like terms aids in the manipulation and interpretation of data. These techniques facilitate the identification of patterns, relationships, and trends in large data sets.

Coding and Computer Science:
Algebraic simplification techniques, including combining like terms and the distributive property, are employed in coding and computer science. They are used to optimize algorithms, simplify equations in programming languages, and enhance computational efficiency.

## FAQs

##### What does it mean to combine like terms?

Combining like terms refers to the process of simplifying an algebraic expression by grouping together terms that have the same variable raised to the same exponent. Terms are considered “like” if they have identical variables and exponents. To combine like terms, you add or subtract the coefficients (the numbers multiplied by the variables) while keeping the variables unchanged.

##### How do I know which terms are like terms?

To identify like terms, examine the variables and their exponents in each term. Terms are considered like terms if they have the same variable(s) raised to the same exponent(s). For example, 3x, 4x, and -2x are like terms because they all have the variable x raised to the first power. Similarly, 2x², -5x², and x² are like terms because they have the variable x raised to the second power.

##### What is the distributive property?

The distributive property is a fundamental property in mathematics that allows us to multiply a value outside parentheses by each term inside the parentheses. It can be stated as follows: a(b + c) = ab + ac. In other words, you distribute the value a to each term inside the parentheses by multiplying. This property is often used to simplify expressions or solve equations involving multiplication.

##### Why are combining like terms and the distributive property important in algebra?

Combining like terms and utilizing the distributive property are essential techniques in algebra. They allow us to simplify expressions, solve equations, and manipulate algebraic formulas more efficiently. By mastering these concepts, students can streamline calculations, identify patterns, and make algebraic manipulations more manageable. Combining like terms and the distributive property provides the foundation for solving complex algebraic problems and understanding higher-level mathematical concepts.

##### How can I practice combining like terms and the distributive property?

To practice combining like terms and the distributive property, you can work on exercises and problem sets that involve simplifying expressions, solving equations, and simplifying algebraic formulas. You can find practice problems in textbooks, online resources, or worksheets specifically designed for these topics. Additionally, creating your own expressions and equations and simplifying them using these concepts will strengthen your understanding and proficiency. Regular practice will enhance your algebraic skills and familiarity with combining like terms and the distributive property. Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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