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Check 13-1 HW

Polynomials. 13-1. Pre-Algebra. Check 13-1 HW. Simplifying Polynomials. 13-2. Pre-Algebra. Pre-Algebra HOMEWORK. Page 654 #15-26. Polynomials. 13-1. Pre-Algebra. Our Learning Goal Students will be able to classify, simplify, add and subtract polynomials. Polynomials. 13-1.

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Check 13-1 HW

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  1. Polynomials 13-1 Pre-Algebra Check 13-1 HW

  2. Simplifying Polynomials 13-2 Pre-Algebra Pre-Algebra HOMEWORK Page 654 #15-26

  3. Polynomials 13-1 Pre-Algebra Our Learning Goal Students will be able to classify, simplify, add and subtract polynomials.

  4. Polynomials 13-1 Pre-Algebra • Students will be able to classify, simplify, add and subtract polynomials by completing the following assignments. • Learn to classify polynomials by degree and by the number of terms. • Learn to simplify polynomials. • Learn to add polynomials. • Learn to subtract polynomials. • …..and that’s all folks!

  5. Simplifying Polynomials 13-2 Pre-Algebra Today’s Learning Goal Assignment Learn to simplify polynomials.

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

  7. Simplifying Polynomials 13-2 x 1 2 2 Pre-Algebra Warm Up Identify the coefficient of each monomial. 1.3x42.ab 3.4. –cb3 Use the Distributive Property to simplify each expression. 5. 9(6 + 7) 6. 4(10 – 2) 3 1 –1 32 117

  8. Simplifying Polynomials 13-2 Pre-Algebra 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

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

  10. Simplifying Polynomials 13-2 3 2 2 3 5x + y + 2 – 6y + 4x Like terms: 3a3b2, 2a3b2, and –a3b2 Like terms: 5x3 and 4x3, y2 and –6y2 3 2 3 2 2 3 2 3 3a b + 3a b + 2a b – a b Identify like terms. Identify like terms. Pre-Algebra Additional Example 1A & 1B: Identifying Like Terms Identify the like terms in each polynomial. A. 5x3 + y2 + 2 – 6y2 + 4x3 B. 3a3b2 + 3a2b3 + 2a3b2 - a3b2

  11. Simplifying Polynomials 13-2 4 2 2 4 4y + y + 2 – 8y + 2y Like terms: 4y4 and 2y4, y2 and –8y2 7n4r2 + 3a2b3 + 5n4r2 + n4r2 Identify like terms. Identify like terms. Pre-Algebra Try This: Example 1A & 1B Identify the like terms in each polynomial. A. 4y4 + y2 + 2 – 8y2 + 2y4 B. 7n4r2 + 3a2b3 + 5n4r2 + n4r2 Like terms: 7n4r2, 5n4r2, and n4r2

  12. Simplifying Polynomials 13-2 7p3q2 + 7p2q3 + 7pq2 There are no like terms. Identify like terms. Pre-Algebra Additional Example 1C: Identifying Like Terms Identify the like terms in the polynomial. C. 7p3q2 + 7p2q3 + 7pq2

  13. Simplifying Polynomials 13-2 There are no like terms. Identify the like terms. Pre-Algebra Try This: Example 1C Identify the like terms in the polynomial. C. 9m3n2 + 7m2n3 + pq2 9m3n2 + 7m2n3 + pq2

  14. Simplifying Polynomials 13-2 Pre-Algebra 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.

  15. Simplifying Polynomials 13-2 4x2 + 2x2– 6x + 7 + 9 2 6x – 6x + 16 Identify like terms. Combine coefficients: 4 + 2 = 6 and 7 + 9 = 16 Arrange in descending order. Pre-Algebra Additional Example 2A: Simplifying Polynomials by Combining Like Terms Simplify. A. 4x2 + 2x2 + 7 – 6x + 9 4x2 + 2x2 – 6x + 7 + 9

  16. Simplifying Polynomials 13-2 Identify the like terms. Combine coefficients: 2 + 5 = 7 and 6 + 9 = 15 Arrange in descending order. Pre-Algebra Try This: Example 2A Simplify. A. 2x3+ 5x3 + 6 – 4x + 9 2x3+ 5x3 – 4x + 6 + 9 2x3+ 5x3 – 4x + 6 + 9 7x3– 4x + 15

  17. Simplifying Polynomials 13-2 3n5m4+ n5m4 –6n3m – 8n3m 3n5m4+ n5m4 –6n3m – 8n3m 4n5m4–14n3m Arrange in descending order. Identify like terms. Combine coefficients: 3 + 1 = 4 and –6 – 8 = – 14. Pre-Algebra Additional Example 2B: Simplifying Polynomials by Combining Like Terms Simplify. B. 3n5m4–6n3m + n5m4 – 8n3m

  18. Simplifying Polynomials 13-2 Arrange in descending order. Identify like terms. Combine coefficients: 2 + 1 = 3 and –7 + –9 = –16 Pre-Algebra Try This: Example 2B Simplify. B. 2n5p4–7n6p + n5p4 – 9n6p 2n5p4+ n5p4 –7n6p – 9n6p 2n5p4+ n5p4 –7n6p – 9n6p 3n5p4–16n6p

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

  20. Simplifying Polynomials 13-2 2 3 3(x + 5x ) 2 3 3 x + 3  5x 2 3 3x + 15x Distributive Property Pre-Algebra Additional Example 3A: Simplifying Polynomials by Using the Distributive Property Simplify. A. 3(x3 + 5x2)

  21. Simplifying Polynomials 13-2 2(x3+ 5x2) 2  x3 + 2  5x2 2x3 + 10x2 Distributive Property Pre-Algebra Try This: Example 3A Simplify. A. 2(x3 + 5x2)

  22. Simplifying Polynomials 13-2 –4(3m3n + 7m2n) + m2n –4  3m3n – 4  7m2n + m2n –12m3n – 28m2n + m2n –12m3n – 27m2n Distributive Property Combine like terms. Pre-Algebra Additional Example 3B: Simplifying Polynomials by Using the Distributive Property Simplify. B. –4(3m3n + 7m2n) + m2n

  23. Simplifying Polynomials 13-2 –2(6m3p + 8m2p) + m2p –2  6m3p – 2  8m2p + m2p –12m3p – 16m2p + m2p –12m3p – 15m2p Distributive Property Combine like terms. Pre-Algebra Try This: Example 3B Simplify. B. –2(6m3p + 8m2p) + m2p

  24. Simplifying Polynomials 13-2 2 2 2(r + rh) = 2r + 2rh Pre-Algebra Additional Example 4: Business Application The surface area of a right cylinder can be found by using the expression 2(r2 + rh), where r is the radius and h is the height. Use the Distributive Property to write an equivalent expression.

  25. Simplifying Polynomials 13-2 2 2 3a(b + c) = 3ab + 3ac Pre-Algebra Try This: Example4 Use the Distributive Property to write an equivalent expression for 3a(b2+ c).

  26. Simplifying Polynomials 13-2 2 2 2x and 5x , z and –3z 2ab2 and –5ab2, 4a2b and a2b 15x2 + 10 6k2 + 8k + 8 12mn2 + 9n 3h3–5h2 + 8h – 9 Pre-Algebra Insert Lesson Title Here Lesson Quiz Identify the like terms in each polynomial. 1. 2x2 – 3z + 5x2 + z + 8z2 2. 2ab2 + 4a2b – 5ab2 – 4 + a2b Simplify. 3. 5(3x2 + 2) 4. –2k2 + 10 + 8k2 + 8k – 2 5. 3(2mn2 + 3n) + 6mn2 6. 4h2 + 3h3 – 7 – 9h2 + 8h – 2

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