1. Objectives The student will be able to: 1. multiply monomials. 2. simplify expressions with monomials.

2. A monomial is a 1.number, 2.variable, or 3.a product of one or more numbers and variables. Examples: 5 y 3x 2 y 3

3. Why are the following not monomials? x + y addition division 2 - 3a Subtraction More than 1 term!

4. Rule 1. Multiplying Monomials When multiplying monomials, you ADD the exponents with same variables and multiply coefficients. a) x 2 x 4 x 2+4Base = xExponent = x6x6 b) (5x 7 )(x 6 ) 5x 13

5. Rule 1. Multiplying Monomials When multiplying monomials, you ADD the exponents with same variables. c) x x (there is no exponent, what do you put?) d) (5x 7 )(5x 7 )(5x 7 ) 125x 21

6. Example1. Simplify m 3 (m 4 )(m) A. m 7 B. m 8 C. m 12 D. m 13 Add exponents Remember you are adding 3 exponents, if an exponent isn’t given, always put a 1 there.

7. Example1b. Simplify 4m 3 (3m)(2m) A. 24m 5 B. 24m 6 C. 24m 4 D. 24m 3 Add exponents Remember you are adding 3 exponents, if an exponent isn’t given, always put a 1 there.

8. Ex2: More examples, with negatives A. (-12abc)(4a 2 b 4 ) *(only 1 c)* B. (-a 2 b 4 ) (1/4a 3 b 5 ) C. (-3a 4 d) (a 5 d 2 ) D. z 5 ½z 2 E. -5z 5 - z 2

9. Example 3: You try Multiply coefficients and ADD exponents with same variable! a)(4ab 6 ) (-7a 2 b 3 ) b)(r 4 )(-12r 7 ) c) (6cd 5 )(5c 5 d 2 ) d) 2a 2 y 3 3a 3 y 4

10. Rule 2. Power to a Power When you have an exponent with an exponent, you multiply those exponents and multiply coefficients. a) (x 2 ) 3 x 2 3 x6x6 b) (y 3 ) 4 y 12

11. Rule 2. Power to a Power When you have an exponent with an exponent, you multiply those exponents and multiply coefficients. c) [(3 2 ) 3 ] 2 d) [(2 3 ) 3 ] 2 Check with the calculator

12. Example 1. Simplify (p 2 ) 4 A. p 2 D. p 4 C. p 8 D. p 16 Multiply exponents!

13. Rule 3. Power of a Product When you have a power outside of the parentheses, everything in the parentheses is raised to that power. a) (2a) 3 DISTRIBUTE (2 arrows) 23a323a3 8a 3 b) (3x) 2 (2 arrows) 9x 2

14. Rule 3. Power of a Product When you have a power outside of the parentheses, everything in the parentheses is raised to that power. c) (2ab) 3 DISTRIBUTE (3 arrows) 23a3b323a3b3 8a 3 b 3 d) (3x4v) 2 (4 arrows) 9x 2 16v 2

15. Example 5. Simplify (4r) 3 A. 12r 3 B. 12r 4 C. 64r 3 D. 64r 4 Draw 2 arrows and DISTRIBUTE.

16. Example 1, You Try: a)(p 1 ) 2 b)(3p 2 ) 4 c)(5xy 2 ) 4 MULTIPLY DISTRIBUTE-2 arrows DISTRUBTE-3 arrows

17. Rule 4. Simplify (all rules) This is a combination of all of the rules. a) (x 3 y 2 ) 4 x 3 4 y 2 4 x 12 y 8 b) (4x 4 y 3 ) 3 64x 12 y 9 C) (2 v 3 w 4 )(3vw 3 ) 2

18. Example 6. Simplify (3a 2 b 3 ) 4 A. 12a 8 b 12 B. 81a 6 b 7 C. 81a 16 b 81 D. 81a 8 b 12 Draw arrows and DISTRIBUTE!

19. Combining terms (-8 v 3 w 4 )(-3vw 3 ) 2 (-5 v 7 w 4 ) 2 (v 3 w 3 ) 2

20. All Rules Combined: 1.x(x 4 )(x 6 ) = 2.(4a 4 b 4 )(9 a 2 b 3 ) = 3.[(2 3 ) 2 ] 3 = 4.(3y 5 z) 2 = 5.(-4mn 2 ) (12m 2 n) = 6.(-2 v 3 w 4 )(-3vw 3 ) 2 =

21. Warm-UP, What to do with the exponents? Add? multiply? 1. y(y 6 ) = 2. (3p 2 ) 4 = 3. (2a 2 )(8a) = 4. (rs)(rs 3 )(s 2 ) = 5. (-4x 3 ) (-5x 7 ) = 6. (-2 v 3 w 4 )(-3vw 3 ) 2 = 7. [(2 3 ) 2 ] 3 =

22. Lets review the 4 rules: 1.When you multiply powers with the same base you______________ 2. When you have a power to a power (powers are side by side and stacked) you ________ 3. When you have a power on the outside of the parenthesis you ___________________ 4. Simplify/combine all the rules.

23. Practice a few more 1.(-10x 3 yz 2 )(-2xy 5 ) = 2.(-x 3 )(-x 4 ) = 3.(2 a 2 )(8a) =

24. Using Geometry How do you find AREA = How do you find VOLUME = Example 1: Express the area of the square as a monomial. What do you remember about a square? Area = 4ab

25. Example 2: Find area 2n 2 5n 3 Area of a triangle: 4ab 5 3a 4 b Area of a triangle: