1. Multiplying monomials with monomial

2. Monomial
An algebraic expression which contains only one term
is known as Monomial 
Example : 2x, 3x2, 4t, 9p2q, -8mn2
While multiplying monomials, do the following steps
Step1:- First split the terms
Step2:- Write all the constants first and then group same variables together
Step3:- Multiply the constants and each of the different variables separately
Step4:- Finally multiply the constants and variables

3. Multiplying Monomials
Example1 : 3a x 4b
Step1:- First split the terms
= 3 x a x 4 x b
Step2:- Write all the constants first and then group variables together
= (3 x 4) x a x b
Step3:- Multiply the constants and each of the different variables separately
=12 x a x b
Step4:- Finally multiply the constants and variables
=12ab
Example2 : 4m x (-5n)
Step1:- First split the terms
= 4 x m x -5 x n
Step2:- Write all the constants first and then group variables together
= (4 x -5) x m x n
Step3:- Multiply the constants and each of the different variables separately
= -20 x m x n
Step4:- Finally multiply the constants and variables
= -20mn

4. Example3 : 3a x 5b x 7c
Step1:- First split the terms
= 3 x a x 5 x b x 7 x c
Step2:- Write all the constants first and then group variables together
= (3 x 5 x 7) x a x b x c
Step3:- Multiply the constants and each of the different variables separately
=105 x a x b x c
Step4:- Finally multiply the constants and variables
=105abc
Example4 : 5t x 7t2
Step1:- First split the terms
= 5 x t x 7 x t x t
Step2:- Write all the constants first and then group variables together
= (5 x 7) x t x t x t
Step3:- Multiply the constants and each of the different variables separately
= 35 x t3
Step4:- Finally multiply the constants and variables
= 35t3

5. Multiplying monomials containing exponents using exponent law
Recap of Exponents Law:
Rule1: Multiplying powers with the same base:
Add the exponents. (am).(an) = am+n
For example: ( a3 )x(a2) = a3+2 = a5
Rule2: Power of a Power:
Multiply the exponents. (am)n = amxn
For example: (a3)5 = a3x5 = a15

6. Multiplying monomials containing exponents using exponent law
Example 1: 2x2 x 3x4
Solution:
Illustrations
Explanation
2x2 x 3x4 =6
First multiply the numerical coefficient
2 x 3 = 6
2x2 x 3x4 =6x6
Next multiply the variables with base x using exponent
law. By rule 1, if bases are same add the exponents.
(i.e., x2 x x4 = x2+4 = x6)
Solution: (2x2).(3x4) = 6x6

7. Solution: -5xy x 3x2y2 x 6x3y3 = -90x6y6
Multiplying monomials containing exponents using exponent law
Example 1: - 5xy x 3x2y2 x 6x3y3
Solution:
Illustrations
Explanation
-5xy x 3x2y2 x 6x3y3 = -90
First Multiply the numerical coefficient
-5 x 3 x 6 = -90
-5xy x 3x2y2 x 6x3y3 = -90x6
Next multiply the variables with base x using exponent
law. By rule 1, add the exponents.
(i.e., x x x2 x x3 = x1+2+3 = x6)
-5xy x 3x2y2 x 6x3y3 = -90x6y6
Next multiply the variables with base y using exponent
law. By rule 1, if bases are same add the exponents.
(i.e., y x y2 x y3 = y1+2+3 = y6)
Solution: -5xy x 3x2y2 x 6x3y3 = -90x6y6

8. Try These Multiply (4a) x (3b) Multiply (-6b4) x (4cd)
Multiply (5h4) x (h5)