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Warm-up Mina p. 10

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  1. Warm-up Mina p. 10 • 24 • 45 • 92 • 73 • 2-4 • 4-5 • 9-2 • 7-3 • 54 • 35 • 72 • 63 After completing the warm-up, check your homework.

  2. Mimio Lesson • Lesson 1 • Lesson 2

  3. Remember! Like terms are constants or terms with the same variable(s) raised to the same power(s). To review combining like terms, see lesson 1-7. CLT Simplify each expression by combining like terms. 1.4x + 2x 2. 3y + 7y 3. 8p – 5p 4. 5n + 6n2 6x 10y 3p not like terms

  4. 5x2+ 4x+1 + 2x2+ 5x+ 2 7x2+9x+3 Polynomials can be added in either vertical or horizontal form. In vertical form, align the like terms and add: In horizontal form, use the Associative and Commutative Properties to regroup and combine like terms. (5x2 + 4x + 1) + (2x2 + 5x+ 2) (5x2 + 4x + 1) + (2x2 + 5x+ 2) = (5x2 + 2x2 + 1) + (4x + 5x) + (1 + 2) = 7x2+ 9x+ 3

  5. To subtract polynomials, remember that subtracting is the same as adding the opposite. To find the opposite of a polynomial, you must write the opposite of each term in the polynomial: –(2x3 – 3x + 7)= –2x3 + 3x– 7

  6. Guided Practice MINA p. 11 Add or subtract. 1. 7m2 + 3m + 4m2 2. (r2 + s2) – (5r2 + 4s2) 3. (10pq + 3p) + (2pq – 5p + 6pq) 4. (14d2 – 8) + (6d2 – 2d +1) 11m2 + 3m (–4r2 – 3s2) 18pq – 2p 20d2 – 2d – 7 5. (2.5ab + 14b) – (–1.5ab + 4b) 4ab + 10b

  7. 8x2 + 3x + 6 Application 6. A farmer must add the areas of two plots of land to determine the amount of seed to plant. The area of plot A can be represented by 3x2 + 7x – 5 and the area of plot B can be represented by 5x2 – 4x + 11. Write a polynomial that represents the total area of both plots of land. (3x2 + 7x – 5) Plot A. (5x2– 4x + 11) Plot B. + Combine like terms.

  8. To multiply monomials and polynomials, you will use some of the properties of exponents that you learned earlier in this chapter.

  9. (6 3)(y3y5)   (3 9)(m m2)(n2 n)   Guided Practice MINA p. 12 Example 1: Multiplying Monomials Multiply. A. (6y3)(3y5) (6y3)(3y5) Commutative & Associative Properties Group factors with like bases together. Multiply. 18y8 B. (3mn2) (9m2n) Commutative & Associative Properties Group factors with like bases together. (3mn2)(9m2n) 27m3n3 Multiply.

  10. 1 æ ö ( ) ( ) 2 2 2 s t t - 12 t s s ç ÷ 4 è ø 1 æ ö ( ) ( ) g g 2 2 2 - 12 s s s t t t ÷ ç 4 ø è Example 1C: Multiplying Monomials Multiply. Commutative & Associative Properties Group factors with like bases together.    Multiply.

  11. Remember! When multiplying powers with the same base, keep the base and add the exponents. x2x3= x2+3 = x5

  12. To multiply a polynomial by a monomial, use the Distributive Property.

  13. Example 2A: Multiplying a Polynomial by a Monomial Multiply. 4(3x2 + 4x – 8) 4(3x2 + 4x – 8) Distribute 4. (4)3x2 +(4)4x – (4)8 12x2 + 16x – 32 Multiply.

  14. Example 2B: Multiplying a Polynomial by a Monomial Multiply. 6pq(2p – q) (6pq)(2p – q) (6pq)2p + (6pq)(–q) Distribute 6pq. (6  2)(p  p)(q)+ (–1)(6)(p)(q  q) Commutative & Associative Properties Group factors with like bases together. 12p2q –6pq2 Multiply.

  15. 1 1 ( ) Distribute . 2 2 2 x y xy 2 x y 6 + x y 8 2 2 1 ö æ ö æ 1 ( ) ( ) 2 2 2 2 x y 6 xy + x y 8 x y ÷ ç ÷ ç 2 2 ø è ø è ö æ ö 1 æ 1 ( ) ( ) ( ) ( ) •6 x2 •x + y •y •8 x2•x2 y •y2 ÷ ç ÷ ç 2 ø è ø 2 è Example 2C: Multiplying a Polynomial by a Monomial Multiply. 1 ( ) 2 2 2 x y 6 + xy 8 x y 2 Commutative & Associative Properties Group factors with like bases together. 3x3y2 + 4x4y3 Multiply.

  16. 1 h2 + 2h 2 Application A triangle has a base that is 4cm longer than its height. a. Write a polynomial that represents the area of the triangle. b. Find the area when the height is 8 cm. 48 cm2

  17. Homework Remember to look at MINA or textbook examples if you get stuck. Also write the problems even the application ones. • p. 487 #’s 25, 27, 29, 31, 33 AND • p. 497 #’s 27, 33, 39, 41, 43, 62

  18. Summary • Mimio 2