How to Simplify Algebraic Expressions
Simplifying an algebraic expression means rewriting it in its most compact equivalent form. The two core moves are combining like terms (terms with the same variable raised to the same power) and expanding brackets with the distributive law.
The Order of Operations for Simplifying
- Clear brackets first: multiply out using the distributive law, e.g. 2(x + 3) becomes 2x + 6.
- Combine like terms: 4x + 7x = 11x, but xยฒ and x stay separate โ different exponents are not like terms.
- Collect constants: plain numbers merge into one, e.g. 8 โ 3 = 5.
Watch the Signs
Most simplification mistakes come from sign errors when expanding brackets: โ(x โ 4) is โx + 4, not โx โ 4. Work slowly through one bracket at a time.
Need to break an expression into factors instead? Try our factoring calculator or the algebra solver.