simplify

To simplify is to say the same thing in fewer words. A simplified expression carries exactly the same value as the original — for every possible value of its variables — but is written in its tidiest, most compact form, with nothing left to combine or cancel.

In practice, simplifying an algebraic expression usually means: remove parentheses by distributing, combine like terms, and reduce any fractions to lowest terms. The end product is shorter but equivalent: 2(x + 3) + 4x simplifies to 6x + 6, and 6/8 simplifies to 3/4. The two forms are interchangeable in any calculation.

Be careful: “simplest” is partly a matter of convention and goal. The fully expanded form and the fully factored form of an expression are both legitimate, and which counts as “simpler” depends on what you are about to do next. Simplifying never changes an expression's value — if it did, you would have made an error, not a simplification.