1. Multiplying Monomials
Lesson 23

2. Remember Power Laws 103 x 102 = 103+2 = 105 (102)3 = 106 10 x 10

3. Power Laws
The rules for multiplying powers with same base still apply when the base is a variable.
a3 x a2 = a2+3 = a5
(a2)3 = a6
a x a x a
a x a
a2 x a2 x a2

4. Multiplying Monomials
To multiply two monomials, multiply their numerical coefficients and multiply their variable ( literal ) coefficients.
(3x2y)(-4x4y3)
= (3)(-4)(x2)(x4)(y)(y3)
= -12x2+4y1+3
= -12x6y4
(3x2)(5x3)
= (3)(5)(x2)(x3)
= 15x2+3
= 15x5

5. More Examples (p)(3p) = (1)(3)(p)(p) = 3p1+1 = 3p2 (-2a)(-4b)
(x2y)(-5x)
= (1)(-5)(x2)(x)(y)
= -5x1+2y
= -5x3y

6. More Examples (7e3)2 = (7)2(e3)2 = (7)(7)(e3*2) = 49e6
Area is found by multiplying the length times the width.
Write an expression for the area.
Solution:
A = L x W
A = (4x)(-2y)
A = (4)(-2)(x)(y)
A = -8xy 4x
-2y

7. TRY THIS!
SIMPLIFY
(a3bc)(4ab2c3)
(-2x3y)(-5xy5)
(6x2y)(3xy2)

8. TRY THIS!
Write the expression for the area

9. Class work
Complete Lesson 23 worksheet