Algebraic Simplification

Simplifying algebraic expressions involves reducing them to their shortest and most manageable form while keeping their value unchanged. This typically involves applying the distributive property, combining like terms, and using exponent rules.

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.

 

Algebra Worksheets
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General Strategy for Simplification

1. Use the Distributive Property to remove parenthesis
   a(b + c) = ab + ac
   Example: 3(x + 4) - 4x = 3x + 12 - 4x
   

2. Apply Exponent Rules: Simplify terms involving exponents.

3. Combine like terms with the same variable and exponent.
   Example: 3x + 12 - 4x = 12 - x
   

4. Factor (if applicable): If the expression is a polynomial, consider factoring it. If it’s a rational expression, factor the numerator and denominator to look for cancellations.
   Check out this lesson on Factoring Techniques.
   Check out this lesson on Simplifying Rational Expressions.

5. Perform remaining arithmetic operations.

6. Present in Standard Form: Often, this means terms are ordered by degree (highest power first) or alphabetically.

Videos

Algebraic GCSE simplification
GCSE Maths - How to Simplify Algebraic Expressions?

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GCSE Maths - How to Simplify Expressions by Collecting Like Terms
Combine Like Terms

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Simplifying Algebraic Expressions With Parentheses & Variables
Combining Like Terms

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