1. D IVIDING M ONOMIALS Chapter 8.2

2. D IVIDING M ONOMIALS Lesson Objective: NCSCOS 1.01 Write equivalent forms of algebraic expressions to solve problems. Students will know how to apply the laws of exponents when they divide monomials.

3. D IVIDING M ONOMIALS Example 1- Simplify: x 4 x 2 Remember: x 4 = x * x * x * x which can also be written as xxxx Therefore x 4 = xxxx x 2 xx Cancel out the number of x’s on the top that are on the bottom xxxx xx What you are left with is your solution: x 2 Rule: When dividing monomials you must subtract the exponents on the bottom from those on the top.

4. Example: Which number is bigger, the top or bottom? x’s will end up where there are more There are three more x’s on the bottom, so the answer is:

5. D IVIDING M ONOMIALS x3x3 x2x2 x5x5 x3x3 x3x3 x3x3 x3x3 x6x6 x3x3 x7x7 1. 2. 3. 4. 5.

6. D IVIDING M ONOMIALS x3x3 x2x2 x3x3 x3x3 x3x3 x5x5 x3x3 x6x6 x3x3 x7x7 1. 2. 3. 4. 5. x x2x2 1 x4x4 x3x3 1 1

7. D IVIDING M ONOMIALS Example 2- Simplify: 4x 5 2x 3 Divide the numbers first: 4 ÷ 2 = 2 Divide the variables second: x 5 /x 3 = x 2 Put the numbers and letters back together for your answer: 2x 2 Rule: When dividing monomials you divide the numbers and letter separately

8. D IVIDING M ONOMIALS 1. 4x 3 2x 2. 9x 5 3x 2 3. 8x 7 24x 4 4x 3 6x 12x 3 2x 6 4. 5.

9. D IVIDING M ONOMIALS 1. 4x 3 2x 2. 9x 5 3x 2 3. 8x 7 24x 4 4x 3 6x 12x 3 2x 6 4. 5. 2x 2 3x 3 3 6 x3x3 3 x3x3

10. D IVIDING M ONOMIALS Example 3- Simplify: x 4 3 x 2 Order of operations says to do what’s inside the parenthesis first! We can reduce the number inside the parenthesis x4x4 x2x2 = x2x2

11. D IVIDING M ONOMIALS Example 3- Therefore: x 4 3 x 2 Write out x 2 three times = (x 2 ) 3 (x 2 )(x 2 )(x 2 ) =x6x6

12. Example 4: Simplify: First we look to see if we can reduce inside the parenthesis In this example we can’t Therefore we have multiply the fraction by itself to take care of the exponent outside

13. Remember when we multiply fractions we multiply the top numbers together and then the bottom numbers Rule: When dividing monomials with and exponent outside the fraction you must reduce the fraction then distribute the exponent to all the numbers inside the parenthesis

14. D IVIDING M ONOMIALS 1. 2. 3. 4. 2 3 5 y3y3 x2x2 3

15. D IVIDING M ONOMIALS 1. 2. 3. 4. 2 3 5 y3y3 x2x2 3 x6x6 x3x3 x 10 x6x6 y9y9 1

16. D IVIDING M ONOMIALS Example 5 Simplify: Solve each variable separately:

17. D IVIDING M ONOMIALS Put it all back together

18. D IVIDING M ONOMIALS 1. 2. 3. 4. x3y3x3y3 x2y2x2y2 x5y3x5y3 x2y5x2y5 6xy 6 3x 3 y 2 5x 8 y 8 15x 4 y 5

19. D IVIDING M ONOMIALS 1. 2. 3. 4. x3y3x3y3 x2y2x2y2 x5y3x5y3 x2y5x2y5 6xy 6 3x 3 y 2 5x 8 y 8 15x 4 y 5 xy x3x3 y2y2 2y 4 x2x2 x4y3x4y3 3

20. D IVIDING M ONOMIALS Example 6: Simplify: 4x 4 – 8x 3 + 6x 2 2x 2 Divide each number from the top with the number on the bottom: – + Notice that the sign between each number stays the same as the signs on the top of the problem 2x 2 4x3

21. D IVIDING M ONOMIALS 1. 2. 3. 3x 5 + 6x 4 + 12x 3 6x 5 – 10x 4 + 22x 3 12x 4 + 6x 3 – 16x 2 3x 3 2x 2 6x 2

22. D IVIDING M ONOMIALS 1. 2. 3. 3x 5 + 6x 4 + 12x 3 6x 5 – 10x 4 + 22x 3 12x 4 + 6x 3 – 16x 2 3x 3 2x 2 6x 2 x 2 + 2x + 4 3x 3 – 5x 2 + 11x 2x 2 + x + 8 3

23. D IVIDING M ONOMIALS 1. 2. 3. 2 x3x3 x5x5 8x 6 3x 3 4x 3 x2x2 5. 4. 6x 6 y 2 3x 3 y 5 24x 5 + 12x 3 – 18x 2 3x 2

24. D IVIDING M ONOMIALS 1. 2. 3. 2 x3x3 x5x5 8x 6 3x 3 4x 3 x2x2 5. 4. 6x 6 y 2 3x 3 y 5 24x 5 + 12x 3 – 18x 2 3x 2 x2x2 2x 3 9x 2 2x 3 y3y3 8x 3 + 4x – 6