Multiplication of Two Monomials is the process of multiplying a Monomial by another Monomial. A monomial is nothing but an expression that consists of only one term in it. x, x^{2}, x^{3}, x^{4}, etc are examples of the monomial. The resultant of the multiplication of monomial by monomial is also a monomial. While multiplying two monomials, the coefficients are multiplied together then the variables are multiplied.

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## Multiplication of Monomial by a Monomial | How to Multiply Two Monomials Together?

As we understand when monomials are multiplied, first we will go through the multiplication of the coefficients then we go through the multiplication of the variables. Check out the process to multiply a monomial by a monomial.

**Method I:**

(i) Firstly, expand the given terms according to their powers.

(ii) Identify the coefficients and variables and multiply them separately.

(iii) Finally, simplify the coefficients and variables and write down the answer.

**Example:**

Multiply 2x^{2}y^{3} and 4x^{3}y^{2}

**Solution:**

Given monomials are 2x^{2}y^{3} and 4x^{3}y^{2}.

Expand the given terms.

= (2 × x × x × y × y × y) × (4 × x × x × x × y × y)

Identify the coefficients and variables and multiply them separately

= (2 × 4) × (x × x × x × x × x) × (y × y × y × y × y)

= 8x^{5}y^{5}

Therefore, the answer is 8x^{5}y^{5}

**Method II:**

(i) Identify the coefficients and variables.

(ii) Multiply the coefficients and prefix their product to the product of letters in the monomials.

(iii) Add the exponents of similar variables or the base.

(iv) At last note down the answer.

**Example:**

Multiply 2x^{2}y^{3} and 4x^{3}y^{2}

**Solution:**

Given monomials are 2x^{2}y^{3} and 4x^{3}y^{2}.

Multiply the coefficients.

= (2 × 4)

Add the exponents of similar variables

= (x^{2 + 3}) × (y^{3 + 2}) = x^{5}y^{5}

Therefore, the answer is 8x^{5}y^{5}

See More: Worksheet on Multiplying Monomial and Polynomial

### Multiplying Monomials Examples

The below problems are on the Multiplication of a Monomial by Monomial. Check how to multiply a Monomial by a Monomial and solve all the problems.

**Question 1.**

Find the product of 8a^{3}b^{4}, b^{3}c^{6}, and 2ac^{3}.|

**Solution:**

Given monomials are 8a^{3}b^{4}, b^{3}c^{6}, and 2ac^{3}.

Expand the given terms.

= (8 × a × a × a × b × b × b × b) × (b × b × b × c × c × c × c × c × c) × (2 × a × c × c × c)

Identify the coefficients and variables and multiply them separately

= (8 × 2) × (a × a × a × a) × (b × b × b × b × b × b × b) × (c × c × c × c × c × c × c × c × c)

= 16a^{4}b^{7}c^{9}

Therefore, the answer is 16a^{4}b^{7}c^{9}

**Question 2.**

Find the product of 3m^{3} with 4m^{2}.

**Solution:**

Given monomials are 3m^{3} and 4m^{2}.

Multiply the coefficients.

= (3 × 4) = 12

Add the exponents of similar variables

= (m^{3 + 2}) = m^{5}

Therefore, the answer is 12m^{5}

**Question 3.**

Find the product of -3p^{2}qr^{3}, 5pq^{3}r^{2,} and -2qr.

**Solution:**

Given monomials are -3p^{2}qr^{3}, 5pq^{3}r^{2,} and -2qr.

Expand the given terms.

= (-3 × p × p × q × r × r × r) × (5 × p × q × q × q × r × r) × (-2 × q × r)

Identify the coefficients and variables and multiply them separately

= (-3 × 5 × -2) × (p × p × p) × (q × q × q × q × q) × (r × r × r × r × r × r)

= 30p^{3}q^{5}r^{6}

Therefore, the answer is 30p^{3}q^{5}r^{6}

**Question 4.**

Multiply 3a, 5a, and 6a.

**Solution:**

Given monomials are 3a, 5a, and 6a.

Multiply the coefficients.

= (3 × 5 × 6) = 90

Add the exponents of similar variables

= (a^{ 1 + 1 + 1}) = a^{3}

Therefore, the answer is 90a^{3}.

### FAQs on Multiplying Two Monomials and then Simplifying the Product

**1. What is Monomial?**

A monomial is an expression that consists of only one term in it.

**2. What are the examples of Monomial?**

The examples of Monomial are x, y, 2y, 2x, y^{2}, x^{2}, etc.

**3. How to multiply monomials?**

Follow the two steps to multiply monomials. When you multiply monomials, multiply the coefficients and then multiply the variables separately. Also, use the laws of exponents wherever you required them.

**4. Is 4y a single term or two terms?**

4y is a single term, hence a monomial.

**5. Can a monomial have more than one variable?**

Yes, a monomial can have more than one variable.

### Summary

The most important thing to get success is the best preparation. You will get the best practice if you prepare with our articles. We have also included different activities for students on every concept. Therefore, the students can learn the concepts practically instead of just reading the theory.