1. 13-2 Simplifying Polynomials Pre-Algebra Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

2. Warm Up Identify the coefficient of each monomial. 1. 3x 4 2. ab 3. 4. –cb 3 Use the Distributive Property to simplify each expression. 5. 9(6 + 7)6. 4(10 – 2) 3 1 –1 x 2 1 2 117 32 Pre-Algebra 13-2 Simplifying Polynomials

3. Problem of the Day Warren drank 3.5 gallons of water in one week. Find the average number of ounces of water Warren drank each day that week. 64 oz Pre-Algebra 13-2 Simplifying Polynomials

4. Learn to simplify polynomials. Pre-Algebra 13-2 Simplifying Polynomials

5. Additional Example 1A & 1B: Identifying Like Terms Identify the like terms in each polynomial. A. 5x 3 + y 2 + 2 – 6y 2 + 4x 3 B. 3a 3 b 2 + 3a 2 b 3 + 2a 3 b 2 - a 3 b 2 Identify like terms. 5x + y + 2 – 6y + 4x 3 2 2 3 Like terms: 5x 3 and 4x 3, y 2 and –6y 2 3a b + 3a b + 2a b – a b 3 2 2 3 3 3 2 2 Identify like terms. Like terms: 3a 3 b 2, 2a 3 b 2, and –a 3 b 2 Pre-Algebra 13-2 Simplifying Polynomials

6. Additional Example 1C: Identifying Like Terms Identify the like terms in the polynomial. C. 7p 3 q 2 + 7p 2 q 3 + 7pq 2 Identify like terms. There are no like terms. 7p 3 q 2 + 7p 2 q 3 + 7pq 2 Pre-Algebra 13-2 Simplifying Polynomials

7. Try This: Example 1A & 1B Identify the like terms in each polynomial. A. 4y 4 + y 2 + 2 – 8y 2 + 2y 4 B. 7n 4 r 2 + 3a 2 b 3 + 5n 4 r 2 + n 4 r 2 Identify like terms. 4y + y + 2 – 8y + 2y 4 2 2 4 Like terms: 4y 4 and 2y 4, y 2 and –8y 2 7n 4 r 2 + 3a 2 b 3 + 5n 4 r 2 + n 4 r 2 Identify like terms. Like terms: 7n 4 r 2, 5n 4 r 2, and n 4 r 2 Pre-Algebra 13-2 Simplifying Polynomials

8. Try This: Example 1C Identify the like terms in the polynomial. C. 9m 3 n 2 + 7m 2 n 3 + pq 2 Identify the like terms. There are no like terms. 9m 3 n 2 + 7m 2 n 3 + pq 2 Pre-Algebra 13-2 Simplifying Polynomials

9. To simplify a polynomial, combine like terms. It may be easier to arrange the terms in descending order (highest degree to lowest degree) before combining like terms. Pre-Algebra 13-2 Simplifying Polynomials

10. Additional Example 2A: Simplifying Polynomials by Combining Like Terms Simplify. A. 4x 2 + 2x 2 + 7 – 6x + 9 Identify like terms. 4x 2 + 2x 2 – 6x + 7 + 9 2 6x – 6x + 16 Combine coefficients: 4 + 2 = 6 and 7 + 9 = 16 Pre-Algebra 13-2 Simplifying Polynomials Arrange in descending order. 4x 2 + 2x 2 – 6x + 7 + 9

11. Additional Example 2B: Simplifying Polynomials by Combining Like Terms Simplify. B. 3n 5 m 4 – 6n 3 m + n 5 m 4 – 8n 3 m Arrange in descending order. Identify like terms. 3n 5 m 4 + n 5 m 4 – 6n 3 m – 8n 3 m Combine coefficients: 3 + 1 = 4 and –6 – 8 = – 14. Pre-Algebra 13-2 Simplifying Polynomials 3n 5 m 4 + n 5 m 4 – 6n 3 m – 8n 3 m 4n 5 m 4 – 14n 3 m

12. Try This: Example 2A Simplify. A. 2x 3 + 5x 3 + 6 – 4x + 9 Identify the like terms.Combine coefficients: 2 + 5 = 7 and 6 + 9 = 15 Pre-Algebra 13-2 Simplifying Polynomials Arrange in descending order. 2x 3 + 5x 3 – 4x + 6 + 9 7x 3 – 4x + 15

13. Try This: Example 2B Simplify. B. 2n 5 p 4 – 7n 6 p + n 5 p 4 – 9n 6 p Arrange in descending order. Identify like terms. Combine coefficients: 2 + 1 = 3 and –7 + –9 = –16 Pre-Algebra 13-2 Simplifying Polynomials 2n 5 p 4 + n 5 p 4 – 7n 6 p – 9n 6 p 3n 5 p 4 – 16n 6 p

14. Sometimes you may need to use the Distributive Property to simplify a polynomial. Pre-Algebra 13-2 Simplifying Polynomials

15. Additional Example 3A: Simplifying Polynomials by Using the Distributive Property Simplify. A. 3(x 3 + 5x 2 ) 2 3(x + 5x ) 3 Distributive Property 2 3  x + 3  5x 3 2 3x + 15x 3 Pre-Algebra 13-2 Simplifying Polynomials

16. Additional Example 3B: Simplifying Polynomials by Using the Distributive Property Simplify. B. –4(3m 3 n + 7m 2 n) + m 2 n Distributive Property –4(3m 3 n + 7m 2 n) + m 2 n –4  3m 3 n – 4  7m 2 n + m 2 n –12m 3 n – 28m 2 n + m 2 n –12m 3 n – 27m 2 n Combine like terms. Pre-Algebra 13-2 Simplifying Polynomials

17. Try This: Example 3A Simplify. A. 2(x 3 + 5x 2 ) 2(x 3 + 5x 2 ) Distributive Property 2  x 3 + 2  5x 2 2x 3 + 10x 2 Pre-Algebra 13-2 Simplifying Polynomials

18. Try This: Example 3B Simplify. B. –2(6m 3 p + 8m 2 p) + m 2 p Pre-Algebra 13-2 Simplifying Polynomials Distributive Property –2(6m 3 p + 8m 2 p) + m 2 p –2  6m 3 p – 2  8m 2 p + m 2 p –12m 3 p – 16m 2 p + m 2 p –12m 3 p – 15m 2 p Combine like terms.

19. Additional Example 4: Business Application The surface area of a right cylinder can be found by using the expression 2(r 2 + rh), where r is the radius and h is the height. Use the Distributive Property to write an equivalent expression. 2(r + rh) = 2 2 r + 2 rh 2 Pre-Algebra 13-2 Simplifying Polynomials

20. Try This: Example 4 Use the Distributive Property to write an equivalent expression for 3a(b 2 + c). 3a(b + c) = 2 3ab + 3ac 2 Pre-Algebra 13-2 Simplifying Polynomials

21. Lesson Quiz Identify the like terms in each polynomial. 1. 2x 2 – 3z + 5x 2 + z + 8z 2 2. 2ab 2 + 4a 2 b – 5ab 2 – 4 + a 2 b Simplify. 3. 5(3x 2 + 2) 4. –2k 2 + 10 + 8k 2 + 8k – 2 5. 3(2mn 2 + 3n) + 6mn 2 6. 4h 2 + 3h 3 – 7 – 9h 2 + 8h – 2 Insert Lesson Title Here 2x and 5x, z and –3z 22 2ab 2 and –5ab 2, 4a 2 b and a 2 b 15x 2 + 10 6k 2 + 8k + 8 12mn 2 + 9n 3h 3 – 5h 2 + 8h – 9 Pre-Algebra 13-2 Simplifying Polynomials