1Cademy - Simplifying $$u^2v + 5u^2

Learn Before

Procedure for Combining Like Terms

Example

Simplifying $u^2v + 5u^2 - 3v^2$

Simplify the expression containing three monomials:

$u^2v + 5u^2 - 3v^2$

Examine each term's variable structure: $u^2v$ contains both $u^2$ and $v$ ; $5u^2$ contains only $u^2$ ; and $-3v^2$ contains only $v^2$ . Although all three terms involve the variables $u$ and/or $v$ , none share the exact same combination of variables with the same exponents. Therefore, there are no like terms to combine, and the expression is already in its simplest form:

$u^2v + 5u^2 - 3v^2$

This example highlights that for terms to be like terms, every variable must appear with the same exponent in each term — merely sharing some variables is not sufficient.

Updated 2026-04-29

Contributors are:

Who are from:

References

Learn Before

Related

Learn After