## How to Multiply Monomials

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The phrase "monomial," as the name implies, is made up of the terms "**mono**" and "**nomial**," which relate to a single expression. A monomial is an algebraic or mathematical phrase consisting of just **one term **with no mathematical operation. Furthermore, the monomial terms can be variables or a mixed term with a **co-efficient**. Furthermore, the variable's power (let's say \(x\)) in a monomial should be an integer, **not **a **fractional **power like the squared or cube root.

For example, \(2x^{\frac{1}{3}}\) is **not **a monomial as the term has a fraction power of \(x\). Now, monomial is a type of polynomial, about which we will learn next.

### Degree of a Monomial

Unlike a polynomial, the degree of a monomial is pretty simple to find. Since a monomial consists of only one term, hence its degree would obviously be the exponent power of that term. So, for example in the term \(4x^3\), we can see that the degree of \(x\) is \(3\). So, the degree of the monomial is considered as \(3\).

Now, for a monomial expression with multiple variables, the case becomes quite complex. So, for example, let’s take the multivariable monomial expression \(3x^2y^3\). Now, here we can clearly see that the monomial has 2 different variables as \(x\) and \(y\). So, what we do here is add up the exponent powers of the separate variables. So, in this case the addition comes as \(2 \ + \ 3 \ = \ 5\). Hence, the degree of this monomial is \(5\).

### Some Rules in Multiplying Monomials

While multiplying monomials, keep the following rules in mind:

- Always remember the sign rules while multiplication. If both
**signs**are the**same**, the resulting sign would be a “**+**”. And, if both**signs**are**opposite**, then the resulting sign would be “**-**“. - Next, while multiplying, the powers of the same variables add up. For example, the multiplication of \(3x^2 \times 2x^3\) gives \(6x^5\) as a result. So, here we can see that the powers \(2\) and \(3\) added up to give \(5\).

### Multiplying Monomials

Let’s understand the multiplication in monomials by the following examples.

- \(3x^2y \times -3x \ = \ 3x^2y \times -3x \ = \ -9x^3y\)
- \(3x^2 \times 12x \ = \ 3x^2 \times 12x \ = \ 36x^3y\)
- \(y \times -9x \ = \ y \ -9x \ = \ -9xy\)
- \(4x^2 \times -3x \ + \ 7x^3 \times 6x^2 \ – \ 5x \times -6x \ = \ -12x^3 \ + \ 42x^5 \ + \ 30x^2\)

### Exercises for Multiplying Monomials

**1) **\(-3x^2y^3z \ \times \ 3x = \)

**2) **\(4x^2y^3z \ \times \ 3x = \)

**3) **\(1xy \ \times \ 2x^2y = \)

**4) **\(6x^2y^2z \ \times \ 3xz^2 = \)

**5) **\(8xy \ \times \ 2x^2y = \)

**6) **\(-1x^2y^2z \ \times \ 4xz^2 = \)

**7) **\(3xy \ \times \ (-3z) = \)

**8) **\(10xy \ \times \ (-2z) = \)

**9) **\(-4xy \ \times \ (-2z) = \)

**10) **\(-8x^2y^2z \ \times \ 7xz^2 = \)

## Multiplying Monomials Practice Quiz

### More Polynomials courses

- How to Classify Polynomials
- How to Write Polynomials in Standard Form
- How to Multiply Monomials
- How to Simplify Polynomials
- How to Add and Subtract Polynomials
- How to Multiply a Polynomial and a Monomial
- How to Multiply Binomials
- How to Do Operations with Polynomials
- How to Factor Trinomials
- How to Divide Monomials