Multiplying and Dividing Monomials

Objectives: Understand the concept of a monomial Use properties of exponents to simplify expressions

Monomial An expression that is either: a variable a product of a constant and 1 or more variables a constant 5, -21, 0 2x, 4ab 2, -7m 3 n 8

Multiply (a 3 b 4 )(a 5 b 2 ) (a 3 a 5 )(b 4 b 2 ) Group like bases When multiplying, add the exponents. Answer: a 8 b 6 Which property was applied?Commutative Property

Multiply (5a 4 b 3 )(2a 6 b 5 )

Multiply (5a 4 b 3 )(2a 6 b 5 ) Multiply the coefficients

Multiply (5a 4 b 3 )(2a 6 b 5 ) 10(a 4 b 3 )(a 6 b 5 ) Group like bases When multiplying, add the exponents. Answer: 10 a 10 b 8 Multiply the coefficients 10(a 4 a 6 )(b 3 b 5 )

Try This! 1. (a 2 b 3 )(a 9 b) Answer: a 11 b 4 2. (3a 12 b 4 )(-5ab 2 )(a 3 b 8 ) Answer: -15 a 16 b 14

Divide a7b5a4ba7b5a4b Group like bases When dividing, subtract the exponents Answer: a 3 b 4 (a )(b ) a7a4a7a4 b5b1b5b1

Divide -30x 3 y 4 -5xy 3 Divide the coefficients. Group like bases Answer: 6 x 2 y (x )(y )

Divide 2m 5 n 4 -3m 4 n 2 Divide the coefficients. Group like bases (m )(n ) 2 -3 Answer: mn2mn2 2 mn =

Try This! 1. m 8 n 5 m 4 n 2 Answer: m 4 n 3 (m )(n ) x 10 y 7 6x 9 y (x )(y ) Answer: -1 2 xy5xy5 - xy 5 2 =

Power of a Product (ab) 2 Rule 4: (xy) n = x n y n (ab)(ab) a2b2a2b2 (ab) 3 (ab)(ab)(ab) a3b3a3b3 Multipy the exponent outside the () times each exponent inside the (). (aa)(bb) (aaa)(bbb)

Power of a Product (a 9 b 5 ) 3 Rule 4: (xy) n = x n y n (a 93 )(b 53 ) Answer: a 27 b 15 (4m 11 n 20 ) 2 (4 12 )(m 112 )(n 202 ) Answer: 16m 22 n 40 (4 1 m 11 n 20 ) 2

xyxy 4 xyxy xyxy xyxy xyxy = x4y4x4y4 Rule 5: xyxy n = xnynxnyn

Try This! 1. (2a 4 ) 3 Rule 4: (xy) n = x n y n (2 13 )(a 43 ) Answer: 8a (4xy 5 z 2 ) 4 (4 14 )(x 14 )(y 54 )(z 24 ) Answer: 256x 4 y 20 z 8 (2 1 a 4 ) 3 (4 1 x 1 y 5 z 2 ) 4

Homework p #5, even, 39, 40