Lesson 1: Simplifying Algebraic Expressions
Lesson 1: Simplifying Algebraic Expressions
Simplify expressions using like terms and the distributive property.
In this lesson you will learn about multiplication properties and their significance.
For example, that a × b = b × a or that a(b + c) = ab + bc.
You will learn how distributive property is used to simplify algebraic expressions. This property is also often used to solve equations. For example, when solving an equation 2(3x – 1) = 10 the first step would be to expand the expression with brackets. It would become 6x – 2 = 10. Then the equation could be solved using inverse operations and reverse BEDMAS.
The lesson covers simplifying algebraic expressions by collecting like terms.
Algebraic expressions are symbols or combinations of symbols used in algebra, containing one or more numbers, variables, and arithmetic operations.
Like terms are terms that have the same variables with the same exponents or no variables – constants (4n and 5n, 6 and 89).
Additional practice will help you master the skills.
Key ideas: Simplifying Algebraic Expressions
To simplify an expression, first use the distributive property to remove brackets, a(b + c) = ab + ac, then collect like terms. To evaluate an expression, substitute the value and follow BEDMAS; put negative values in brackets.
Worked examples
Example 1
Expand 2(x + 4).
- 2x + 8
Example 2
Simplify 3(2a − 5) + 4a.
- 6a − 15 + 4a.
- 10a − 15
Example 3
Simplify 5(x + 2) − 2(x − 3).
- 5x + 10 − 2x + 6 (−2 × −3 = +6).
- 3x + 16
Example 4
Evaluate 3x2 − 2x + 1 when x = −2.
- 3(−2)2 − 2(−2) + 1 = 3(4) + 4 + 1.
- 17
Common mistakes
- Multiplying only the first term in the bracket.
- Sign errors with a negative in front of a bracket.
- Writing −22 instead of (−2)2 when substituting.
Questions students ask
Why put negative numbers in brackets when substituting?
So the exponent and the sign are applied correctly: (−2)2 = 4, but −22 = −4.
Simplifying Expressions Quiz
Check your understanding
Try the quiz for this lesson. You’ll see right away if each answer is correct.