Simplifying algebraic expressions
Collect like terms, apply the distributive law, and keep algebra tidy for later equation work.
Key formulas
Like terms
Only like terms can be added or subtracted. 3x and 5x are like; 3x and 3x² are not. Coefficients combine; the variable part stays the same.
Distributive law
Multiply every term inside a bracket by the factor outside: k(a + b) = ka + kb. Watch the sign when the factor is negative: −2(x − 3) = −2x + 6.
Removing brackets in longer expressions
Expand first, then collect like terms. Write powers in descending order for reading clarity: x² terms, then x terms, then constants.
Exam habit
Underline like terms in different colours (or with different marks) before combining.
Worked example
Expand and collect
Problem. Simplify 4(2x − 3) − 3(x − 5).
Solution. 8x − 12 − 3x + 15 = 5x + 3.
Review quiz
1 / 47x − 3x + 5 − 9 =
Practice questions
- Simplify 7x − 3x + 5 − 9.
- Expand and simplify 3(2x − 4) − 2(x + 1).
- Simplify 4a² + 3a − a² + 5a.
Study notes
Can I add 2x and 2y?
No — they are unlike terms. Leave them as 2x + 2y or factor as 2(x + y) if useful.
What does “simplify” mean?
Expand brackets if needed and collect like terms; usually do not factor unless asked.