Algebraic Expressions
Factorize and simplify algebraic expressions
Algebraic Expressions
An algebraic expression is a mathematical phrase that contains numbers, variables (like x or y), and operations (like +, -, ×, ÷). For example: 3x + 5, 2a² - 4a + 1.
Factorisation
Factorisation is the reverse of expanding. We write an expression as a product of factors.
Common factor: 6x + 9 = 3(2x + 3)
Difference of squares: x² - 25 = (x + 5)(x - 5)
Trinomials: x² + 5x + 6 = (x + 2)(x + 3)
Example
Worked Examples
Factorise: 4x² - 16
Step 1: Common factor of 4 → 4(x² - 4)
Step 2: Difference of squares → 4(x + 2)(x - 2)
Simplify: (x² - 9)/(x + 3)
Factorise numerator: (x + 3)(x - 3)/(x + 3)
Cancel: x - 3 (where x ≠ -3)
Note
Key Rules
Always look for a common factor first.
Remember: a² - b² = (a + b)(a - b)
For trinomials ax² + bx + c: find two numbers that multiply to ac and add to b.
Key Vocabulary
VariableA letter representing an unknown number
ExpressionA combination of numbers, variables, and operations
FactoriseTo write as a product of factors
TermA part of an expression separated by + or -
CoefficientThe number in front of a variable
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