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Section 7.8

FOIL. FOIL. Section 7.8 . Multiplying Polynomials. FOIL. FOIL. California Standards. 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Student solve multistep problems, including word problems, by using these techniques. . (6 3) (y 3 y 5 ). . .

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Section 7.8

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  1. FOIL FOIL Section 7.8 Multiplying Polynomials FOIL FOIL

  2. California Standards 10.0 Students add, subtract, multiply, and divide monomials and polynomials. Student solve multistep problems, including word problems, by using these techniques.

  3. (6 3)(y3 y5)   (3 9)(m m2)(n2 n)   Let’s Try Multiplying Monomials Multiply. A. (6y3)(3y5) (6y3)(3y5) Group factors with like bases together. Multiply. 18y8 B. (3mn2) (9m2n) Group factors with like bases together. (3mn2)(9m2n) Multiply. 27m3n3

  4. Review of Distributive Property 3(x + 7) = 3(x) + 3(7) = 3x + 21 -2(-3 + 4y) = -2(-3) + -2(4y) = 6 + -8y

  5. Multiplying Monomials and Polynomials 4(3x2 + 4x – 8) 4 (3x2 + 4x – 8) Distribute 4. (4)3x2 + (4)4x – (4)8 Multiply. 12x2 + 16x – 32

  6. FOIL

  7. FOIL (2x + 1)(x – 5)

  8. FOIL (3x - 5)(2x + 7)

  9. FOIL (3x - 5)(2x + 7)

  10. The box method ( )( ) 3x +5 4x +6 12x2 20x 30 18x 12x2 + 38x + 30

  11. The box method ( )( ) 6x + 1 3x - 2 18x2 3x -2 -12x 18x2 - 9x - 2

  12. The box method ( )( ) 2x - 3 4x - 2 8x2 -12x 6 -4x 8x2 - 16x + 6

  13. The box method ( )( ) 5x - 4 4x2 +3x - 2 20x3 15x2 -10x -16x2 -12x 8 20x3 - x2 - 22x + 8

  14. Challenge Multiply. (x – 5)(x2 + 4x – 6) Distribute x and –5. (x – 5 )(x2 + 4x – 6) Distribute x and −5 again. x(x2 + 4x – 6) – 5(x2 + 4x – 6) x(x2) + x(4x) + x(–6) – 5(x2) – 5(4x) – 5(–6) Simplify. x3 + 4x2 – 6x – 5x2 – 20x + 30 Combine like terms. x3 – x2 – 26x + 30

  15. Practice Problems • Fill in the blank. • (5a + 2)(6a – 1) = a2 + 7a – 2 • (2x + 9)(x + 2) = 2x2 + x + 18 • (x + 3)2 = x2 + + 9 30 13 6x

  16. (4x + 3)(3x + 2) (2x + 8)(6x + 2) (12x + 3)(x + 1) (6x + 4)(2x + 4) 12x2 + 15x + 3 12x2 + 52x + 16 12x2 + 32x + 16 12x2 + 17x + 6 Match D B A C

  17. (x + 2)(x + 5) (2x + 1)(x + 2) (2y + 1)(3y + 4) Find Each Product 1. 4. (2x + 3)(x + 5) (10x + 10)(2x + 2) (x + 7)2 2x2 + 13x + 15 x2 + 7x + 10 2. 5. 20x2 + 40x + 20 2x2 + 5x + 2 3. 6. x2 + 14x + 49 6y2 + 11y + 4

  18. Lesson Quiz Multiply. 1. (6s2t2)(3st) 2. 4xy2(x + y) 3. (x + 2)(x – 8) 4. (2x – 7)(x2 + 3x – 4) 5. 6mn(m2 + 10mn – 2) 6. (2x – 5y)(3x + y) 18s3t3 4x2y2 + 4xy3 x2 – 6x – 16 2x3 – x2 – 29x + 28 6m3n + 60m2n2 – 12mn 6x2 – 13xy – 5y2

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