Expanding Algebraic Expressions

What is Expanding Algebraic Expressions?

Expanding algebraic expressions is the process of removing the parentheses by distributing the terms inside the parentheses across the terms outside. This allows the expression to be written as a sum or difference of terms without any parentheses.

Steps to Expand Algebraic Expressions

Identify the terms inside the parentheses and the term outside the parentheses.
Multiply the term outside the parentheses by each term inside the parentheses.
Simplify the expression by combining like terms, if necessary.

Examples

Example 1:

Expand the expression: 2(x + 3)

Solution:

Step 1: Multiply the 2 by each term inside the parentheses.

2 times x = 2x

2 times 3 = 6

Step 2: Write the expanded expression.

Expanded Expression: 2x + 6

Example 2:

Expand the expression: 3(2y - 5)

Solution:

Step 1: Multiply the 3 by each term inside the parentheses.

3 times 2y = 6y

3 times -5 = -15

Step 2: Write the expanded expression.

Expanded Expression: 6y - 15

Example 3:

Expand the expression: -4(3a + 7)

Solution:

Step 1: Multiply the -4 by each term inside the parentheses.

-4 times 3a = -12a

-4 times 7 = -28

Step 2: Write the expanded expression.

Expanded Expression: -12a - 28

Exercises

Exercise 1:

Expand the expression: 5(x - 2)

Exercise 2:

Expand the expression: -3(4y + 9)

Exercise 3:

Expand the expression: 6(2m - 3n)

Solutions to Exercises

Solution 1:

Expanded Expression: 5x - 10

Solution 2:

Expanded Expression: -12y - 27

Solution 3:

Expanded Expression: 12m - 18n

Lesson Summary

In this lesson, we learned how to expand algebraic expressions by distributing the term outside the parentheses across the terms inside. We also practiced simplifying the expressions where necessary. Remember, expanding is all about removing parentheses and rewriting the expression as a sum or difference.

Homework

Expand the following expressions:

4(3x + 2)
-2(5y - 4)
7(6a - 9)

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