Algebraic Expressions
Simplify and evaluate algebraic expressions
What are Algebraic Expressions?
An algebraic expression uses letters (variables) to represent unknown numbers, combined with operations (+, −, ×, ÷). For example: 3x + 5 means 'multiply x by 3, then add 5'. Expressions do NOT have an equals sign (that would be an equation).
Example
Writing Expressions
A number plus 7: x + 7
Double a number: 2x
Three less than a number: x − 3
Five times a number, increased by 2: 5x + 2
A number squared: x^2
Simplifying Expressions
Like terms have the same variable and power. We can only add or subtract like terms.
3x + 5x = 8x (both are 'x' terms)
4x^2 + 2x − x^2 + 3x = 3x^2 + 5x (group like terms)
Unlike terms such as 2x and 3y CANNOT be combined.
Example
Substitution
If x = 4, find the value of 2x + 3:
2(4) + 3 = 8 + 3 = 11
If a = 2 and b = 5, find 3a + 2b − 1:
3(2) + 2(5) − 1 = 6 + 10 − 1 = 15
Note
Remember
Only like terms can be combined. When substituting, replace every instance of the variable with the given value and follow the order of operations (BODMAS).
Key Vocabulary
VariableA letter that represents an unknown number
ExpressionA combination of numbers, variables, and operations
Like termsTerms with the same variable and exponent
SubstituteTo replace a variable with a number
SimplifyTo combine like terms into a shorter expression
CoefficientThe number in front of a variable
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