Simplifying Algebraic Expressions

In this lesson, we will learn how to simplify algebraic expressions by combining like terms and using the distributive property.

The following diagram shows how to simplify algebraic expressions by using the distributive rule an combining like terms. Scroll down the page for more examples and solutions on simplifying algebraic expressions.

 

Remember to use order of operations to simplify and be careful with the minus signs.

1. Applying the Distributive Property:
   The distributive property states that (a(b + c) = ab + ac). This means you multiply the term outside the parentheses by each term inside the parentheses.

Examples:
\( 2(x + 3) = 2 \cdot x + 2 \cdot 3 = 2x + 6 \)
\( -4(y - 5) = -4 \cdot y + (-4) \cdot (-5) = -4y + 20 \)
\( a(2a + b - 1) = a \cdot 2a + a \cdot b + a \cdot (-1) = 2a^2 + ab - a \)
\( -(x + 2) = -1(x + 2) = -1 \cdot x + (-1) \cdot 2 = -x - 2 \)

2. Combine like terms that have the same variable and exponent.
   Example:
   \( 4x + 2y − x + 3 = (4x − x) + 2y + 3 = 3x + 2y + 3 \)

Distributive, Like Terms, Simplifying Algebraic Expressions (Introductory Algebra 6)
Using the distributive property, combining like terms, simplify an algebraic expression

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Subtraction (Introductory Algebra 8)
Subtract two numbers, adding and subtracting in problems with several numbers, adding and subtracting within algebraic expressions

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Simplify algebraic expressions using the distributive property and combining like terms

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How to Simplify Algebraic Expressions?

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