Multiplying Monomial
Multiplying monomials follow almost the same method as the multiplication of integers. To multiply monomials with polynomials(binomials or trinomials), we use the distributive property whereby the monomial is multiplied by each term in the other polynomial. The resulting polynomial is simplified further by adding or subtracting the identical terms.
1.  What is Multiplying Monomial? 
2.  Multiplying Monomial by a Monomial 
3.  Multiplying Monomial by a Binomial 
4.  Multiplying Monomial by a Trinomial 
5.  Multiplying Monomial Examples 
What is Multiplying Monomial?
Multiplying monomial is a method for multiplying a monomial with other polynomials. A monomials is referred to as a type of polynomials with just one term, consisting of a variable and its coefficient. The monomial is multiplied with the individual terms of the polynomial and then simplified further to get the resultant polynomial. To multiply polynomials, the coefficient is multiplied with a coefficient, and the variable is multiplied with a variable.
Multiplying Monomial by a Monomial
When a monomial is multiplied by another monomial, their product will be a monomial only. A monomial is an expression that has only one term in it. The coefficients of the monomials are multiplied together and then the variables are multiplied. For example, the product of two monomials, say 2x and 2y is equal to 4xy.
In case, both the monomials have the same variables with the same exponents, then the laws of exponents are used.
Example: Multiply 2x^{3} with 3x^{2}
 Step 1: First we will multiply the coefficients i.e., 2 × 3 = 6
 Step 2: Next, we will multiply the variables but in this case, the powers of both the variables will be added as per the rules of exponents i.e., x^{3} × x^{2} = x^{5}
The final answer is 2x^{3} × 3x^{2} = 6x^{5}
Multiplication of Three or More Monomials
To find the product of more than two monomials, multiply the first two monomials, then multiply the product of these two by the third monomial. The same procedure is repeated for multiplying any number of monomials.
Multiplying Monomial by a Binomial
Binomials are also kind of polynomials consisting of only two terms. A binomial is defined as an algebraic expression consisting of two terms that are separated by the arithmetic signs, either the addition sign (+) or subtraction sign (). When multiplying a monomial by a binomial, we follow the distributive law of multiplication. Let's take an example.
Example: Multiply (3x) (2x – 9)
Solution:
Steps to solve (3x) (2x – 9):
 Step 1: Multiply the monomial with the first term of the binomial.
= (3x) * (2x) = 6x ^{2}
 Step 2: Multiply the monomial with the second term of the binomial.
= (3x) *(9) = 27x
 Step 3: Write both the terms obtained in step 1 and step 2 together with their corresponding signs.
= 6x ^{2 } 27x
Multiplying Monomial by a Trinomial
Trinomials are a particular kind of polynomials consisting of three terms. A trinomial is defined as an algebraic expression consisting of three terms separated by arithmetic symbols/signs, either the addition sign (+) or subtraction sign (). When multiplying a monomial by a trinomial, we follow the distributive law of multiplication. Let's take an example.
Example: Multiply (2x^{2}) (3x+9xy6)
Solution:
Steps to solve (2x^{2}) (3x+9xy6):
 Step 1: Multiply the monomial with the first term of the trinomial.
= (2x^{2}) * (3x) = 6x^{3}
 Step 2: Multiply the monomial with the second term of the trinomial.
= (2x^{2}) *(9xy) = 18x^{2}y
 Step 3: Multiply the monomial with the third term of the trinomial.
= (2x^{2}) *(6) = 12x^{2}
 Step 4: Write all the three terms together with their corresponding signs.
= 6x^{3 }+ 18x^{2}y 12x^{2}
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Multiplying Monomial Examples

Example 1: Using the multiplying monomial rule, multiply 11x and 2x.
Solution:
Given: Monomials, 11x and 2x.
 Step 1: In the above monomials, the common variable is x. We will multiply the variable with the variable. Hence, we get x × x = x^{2}.
 Step 2: Multiply the coefficients of both the monomials to get 11 × 2 = 22.
Thus, multiplying the polynomials 11x and 2x gives 22x^{2} as the result.

Example 2: Multiply (2x)(4x^{2}+7)
Solution:
Given: A monomial and a binomial, 2x and 4x^{2}+7.
 Step 1: Multiply the monomial 2x with the first term of the given binomial, which is 4x^{2}. Hence, we get 2x × 4x^{2} = 8x^{2}.
 Step 2: Multiply the monomial 2x with the second term of the given binomial, which is 7. Hence, we get 2x × 7 = 14x.
Thus, multiplying the polynomials 2x and 4x^{2}+7 gives 8x^{2} + 14x as the result.
FAQs on Multiplying Monomial
What Is Multiplying Monomial in Algebra?
Multiplying Monomial is a method for multiplying a monomial with a polynomial. For multiplying monomials with polynomials(binomials or trinomials), we use the distributive property.
 Step 1: The monomial is multiplied by each of the terms in the other polynomial.
 Step 2: The resulting polynomial is then simplified.
What Is the Method for Multiplying a Monomial by a Monomial?
When multiplying monomials, follow the steps as given below:
 Step 1: Multiply the coefficients
 Step 2: Multiply the variables by adding the exponents.
 Step 3: Write the product so obtained
Note: When multiplying monomials with the same base, the base will remain the same, just add their exponents.
What Is the Product Rule for Multiplying Monomials?
As per the rule, multiply the coefficients first and then multiply the variables by adding the exponents. When monomials with the same base are multiplied, their exponents get added.
How To Solve Multiplying Monomials?
For multiplying a monomial with a polynomial, we usually follow distributive law.
 When multiplying two monomials, we rewrite the product as a single monomial using properties of multiplication and exponents.
 When multiplying a monomial with a binomial, we follow the distributive law of multiplication and we get a binomial as the product.
 When multiplying a monomial with a trinomial, we follow the distributive law of multiplication and we get a trinomial as the product.
What Are the Steps for Multiplying a Monomial by a Binomial?
When multiplying monomial by binomial, we follow the distributive law of multiplication.
 Multiply the monomial with the first term of binomial.
 Multiply the monomial with the second term of binomial.
 Write both the terms together with their corresponding signs.
Give the Steps for Multiplying a Monomial by a Trinomial?
When multiplying monomial by trinomial, we follow the distributive law of multiplication.
 Multiply the monomial with the first term of trinomial.
 Multiply the monomial with the second term of trinomial.
 Multiply the monomial with the third term of trinomial.
 Write all the three terms together with their corresponding signs.
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