Multiplying monomials with monomial

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

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

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

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

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

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

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