Combining Like Terms & Distributing
Two skills that always show up together: distributing a number across parentheses, and combining the like terms that result. Every algebra lesson on this site assumes you can simplify an expression like this before doing anything else with it.
Like terms have the exact same variable raised to the exact same power — 3x and 5x are like terms, but 3x and 5x² aren’t (different powers), and 3x and 3y aren’t (different variables). Only like terms can be combined, by adding or subtracting their coefficients. The distributive property — a(b + c) = ab + ac — is usually the step that creates like terms to combine in the first place: multiply the outside number by every term inside the parentheses, one at a time.
Distributing and combining are two separate moves, done in order — distribute first to clear the parentheses, then look for like terms to combine.
Start with 3(2x − 4) + 5x. First, distribute the 3 across (2x − 4).
A negative sign in front of the parentheses distributes too — it flips the sign of every term inside, not just the first one: