🧩 Algebraic Expressions (Two-step)
Only like terms (same variable AND same exponent) can be combined
▶ Play Door 4Combining Like Terms
Like terms have the same variable raised to the same power. Constants (plain numbers) are also like terms with each other.
ExpressionLike TermsUnlike Terms4x + 2x4x and 2x (same variable)—3x + 2y—3x and 2y (different variables)5x² + 3x—5x² and 3x (different powers)Rules for combining like terms:
• Add or subtract the coefficients only
• The variable part stays unchanged
• Always carry the sign (+ or -) with each term
Worked example
Problem: Simplify: 7a + 3b - 2a + 4b
- Group like terms: (7a - 2a) + (3b + 4b) = 5a + 7b
Answer: Group like terms: (7a - 2a) + (3b + 4b) = 5a + 7b
Distributive Property & Factoring
Distributive Property: Multiply a number outside parentheses by each term inside.
a(b + c) = ab + ac
Factoring is the reverse of the distributive property — find the Greatest Common Factor (GCF) and pull it out.
ab + ac = a(b + c)
To factor, ask: what is the largest number/variable that divides all terms evenly?
Worked example
Problem: Simplify: 5(3x + 4)
- 5 x 3x + 5 x 4 = 15x + 20
Answer: 5 x 3x + 5 x 4 = 15x + 20