sign of a term

Every term in an expression comes with a direction — a plus or a minus — much like a thermometer reading can be above or below zero. The sign of a term tells you whether that piece adds to the total or subtracts from it.

When you read an expression as a sum of terms, the operation sign directly in front of each term belongs to that term. In 4x - 7y + 2, the terms are +4x, -7y, and +2; the leading 4x is understood to be positive. Keeping the sign glued to its term is what makes rearranging and combining safe — moving a term around carries its sign with it.

Most simplification mistakes are sign mistakes. When a minus sits in front of a parenthesis, it flips the sign of every term inside as the parenthesis is removed: -(a - b) becomes -a + b. Always treat the sign as part of the term, never as a stray symbol you can ignore.