literal coefficient

Every term splits into two pieces: a number part and a letter part. If the numerical coefficient is the “how many,” the literal coefficient is the “of what.” In 7xy, the 7 is the numerical coefficient and xy is the literal coefficient — the variable part of the term.

The word “literal” here means “made of letters.” The literal coefficient gathers all the variables of a term, with their exponents: in -3a^2b the literal coefficient is a^2b. It is exactly this part that must match for two terms to be like terms — same letters, same powers — which is why identifying it matters when you combine terms.

Be careful not to confuse the two coefficients. The literal coefficient never includes the leading number or its sign; those belong to the numerical coefficient. And a bare constant such as 9 has no literal coefficient at all, since it carries no variable part.