Algebraic Expressions
Expand and simplify expressions with variables
Expanding and Simplifying Expressions
An algebraic expression contains variables, numbers and operations. To simplify, collect like terms. To expand, use the distributive property: a(b + c) = ab + ac.
Example
Collecting Like Terms
3x + 5y − 2x + 4y
= (3x − 2x) + (5y + 4y)
= x + 9y
2a² + 3a − a² + 5a
= (2a² − a²) + (3a + 5a)
= a² + 8a
Example
Expanding Brackets
3(2x + 4) = 6x + 12
−2(x − 5) = −2x + 10
(x + 3)(x + 2) = x² + 2x + 3x + 6 = x² + 5x + 6
Note
Remember
Like terms have the same variable raised to the same power: 3x and 5x are like terms, but 3x and 3x² are NOT. When expanding, multiply every term inside the bracket by the term outside.
Key Vocabulary
VariableA letter representing an unknown number (e.g. x, y)
CoefficientThe number in front of a variable (e.g. 3 in 3x)
Like termsTerms with the same variable and exponent
ExpandMultiply out brackets
SimplifyWrite in simplest form by collecting like terms
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