Monomial
In short: A monomial is one algebraic term in a single chunk, like 9, a, or 6x²y, with no plus or minus sign inside and only counting-number exponents.
Algebra 1AlgebraA-SSE.A.1a
What is Monomial?
Anything that is one chunk, with no plus or minus sign separating pieces, is a monomial. The number 9, the letter \(a\), and the product \(6x^2y\) all qualify.
In \(6x^2y\), the coefficient is 6 and the variable part is \(x^2y\). The degree is the sum of the exponents, \(2 + 1 = 3\). A variable in a denominator, or a negative or fractional exponent, disqualifies an expression, so \(\frac{5}{x}\) and \(\sqrt{x}\) fail.
How to spot it
- An expression is one piece, with variables multiplied together and no addition or subtraction between pieces.
- A problem asks for the coefficient, the variable part or the degree of one term.
- Two terms such as \(3x^2y\) and \(-4xy^3\) must be multiplied or divided.
- A rule uses this name for the building blocks of a larger expression.
The method
- Confirm there is no plus or minus sign joining separate pieces.
- Read the coefficient, the number in front, and the variable factors with their exponents.
- To find the degree, add the exponents of all variables in the term.
- To multiply two of them, multiply the coefficients and add the exponents of matching variables.
Monomial: solved example
Problem
A storage cube is built from panels, and two monomials describe its parts: \(3x^2y\) and \(-4xy^3\). Find their product and its degree.
Solution
Multiply coefficients: \(3 \cdot (-4) = -12\). Add exponents of x: \(2 + 1 = 3\). Add exponents of y: \(1 + 3 = 4\).
The product is \(-12x^3y^4\), which has degree \(3 + 4 = 7\).
Try it
Question 1
Is \(\frac{x}{3}\) a monomial? Is \(\frac{5}{x}\)?
Show the answer
\(\frac{x}{3} = \frac{1}{3}x\) does, being a number times x. \(\frac{5}{x}\) does not, since x is in the denominator.
Question 2
Simplify \((-2m^3)(5m^4)\).
Show the answer
\(-2 \cdot 5 = -10\) and \(m^{3+4} = m^7\), so \(-10m^7\).
Monomial vs. Term
Every monomial is one term, but the word term is broader: a term may carry anything that sits between plus and minus signs in any expression. The name monomial promises extra rules, namely whole-number exponents and no variables below a fraction bar.
Keep going
Lessons
Worksheets and quizzes
- Adding, Subtracting and Multiplying Polynomials – Worksheet
- Adding, Subtracting and Multiplying Polynomials – Quiz
- Structure of Algebraic Expressions – Worksheet
- Structure of Algebraic Expressions – Quiz
Related words
Whole dictionary: A–Z · Algebra 1 · Algebra