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Mastering Polynomial Multiplication: Distributive Property, FOIL, and Magic Box Methods

This instructional guide focuses on multiplying polynomials using three essential methods: the Distributive Property, FOIL method, and Magic Box method. Through step-by-step examples and exercises, students will learn to expand polynomials effectively and solve related area problems. Key concepts such as coefficients, linear terms, and quadratic terms are clearly explained. The material includes various practice problems, answers, and tips for mastering polynomial multiplication in preparation for quizzes and tests.

francis-sargent
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Mastering Polynomial Multiplication: Distributive Property, FOIL, and Magic Box Methods

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  1. Dispatch 4b2 + 9b 10x2 – 19x + 63 64a6b9c6 Simplify b ( 4b – 1) + 10b x ( 3x – 5 ) + 7 ( x2 – 2x + 9) 3. (4a2b3c2)3

  2. Multiplying Polynomials Objective: We will be able to multiply polynomials using the Distributive Property, FOIL Method, and Magic Box Method. Standard: 10.0

  3. Concept Task (x + 3)(x + 2) x2 + 5x + 6 (8d + 3)(5d + 2) 40d2 + 31d + 6

  4. DISTRIBUTIVE PROPERTY GP (x + 3)(x + 2) Step 1: DP (x + 3)(x + 2) = x(x) + x(2) + 3(x) + 3(2) x2 + 2x + 3x + 6 Step 2: CLT x2 + 5x + 6

  5. LETS REVIEW SOME VOCABULARY Coefficient (x + 3)(x + 2) x2 + 5x + 6 Linear Term Quadratic Term Constant Term

  6. (4h – 2)(4h – 1) YT (2m + 2)(3m – 3) 6m2 – 6 (y – 2)(y + 8) y2 + 6y - 16 The length of a rectangle is 4h + 5and width h + 7. What is the area? 4h2 + 33h + 35

  7. F: First Term O: Outer Term I: Inner Term L: Last Term FOIL METHOD GP (y + 4)(y – 3) (y + 4)(y – 3) F (y)(y) O (y)(-3) I (4)(y) L (4)(-3) y2 -3y + 4y - 12 y2 + y - 12

  8. F: First Term O: Outer Term I: Inner Term L: Last Term FOIL METHOD GP (7x – 4)(5x – 1) (7x – 4)(5x – 1) F (7x)(5x) O (7x)(-1) I (-4)(5x) L (-4)(-1) 35x2 – 7x-20x + 4 35x2 -27x + 4

  9. F: First Term O: Outer Term I: Inner Term L: Last Term YT (2w – 5)(w + 7) 2w2 + 9w – 35 (5m – 6)(5m – 6) 25m2– 60m+ 36

  10. MAGIC BOX METHOD GP (p – 4)(p + 2) p – 4 X p +2 p2 -4p 2p -8 p2 – 2p – 8

  11. MAGIC BOX METHOD GP (5a – 2)(2a– 3) 5a – 2 X 2a – 3 10a2 -4a – 15p 6 10a2 – 19p +6

  12. YT (3c +1)(c – 2) (d – 1)(5d – 4) (4c + 1)(2c + 1)

  13. MAGIC BOX METHOD GP (3c +1)(c – 2) 3c +1 X c – 2 3c2 c -6c -2 3c2 – 5c – 2

  14. MAGIC BOX METHOD GP (d– 1)(5d – 4) d – 1 X 5d – 4 5d2 –5d -4d 4 5d2 – 9d+4

  15. MAGIC BOX METHOD GP (4c + 1)(2c + 1) 4c + 1 X 2c +1 8c2 2c 4c 1 8c2+ 6c+1

  16. Daily Practice Study Guide Intervention Worksheet Pg. 97 1-18 EVEN REMINDER: QUIZ TOMORROW PERIOD 1 1/18/13 REMINDER: TUTORING TODAY 3:50-4:50 LIBRARYGET EXTRA POINTS!!!

  17. What if we have….. (p + 4)(p2 + 2p – 7) p( p2 + 2p – 7) + 4(p2 + 2p – 7) (8p) (-28) (-7p) (p3) + (2p2) (4p2) p3+ 6p2 + p – 28

  18. F: First Term O: Outer Term I: Inner Term L: Last Term YT (2w – 5)(w + 7) 2w2 + 9w – 35 (5m – 6)(5m – 6) 25m2– 60m+ 36 The length of a rectangle is 10r – 4. The width is 10r + 4. What is the Area of the Rectangle? 100r2 – 16

  19. A B C D A.Find (x + 2)(x – 3). A.x2 + x – 6 B.x2 – x – 6 C.x2 + x + 6 D.x2 + x + 5

  20. A B C D B. Find (3x + 5)(2x – 6). A. 5x2 – 8x + 30 B. 6x2 + 28x – 1 C. 6x2 – 8x – 30 D. 6x – 30

  21. Dispatch PA #3 Problems -5p3 – 9p2 + 5p Write an expression to represent the area of the rectangle 2x – 5 x + 4 Area= 2x2 + 3x – 20 Simplify Subtract (6p3 + 3p2 – 7p) from (p3 – 6p2 – 2p) 2.

  22. LETS REVIEW F: First Term O: Outer Term I: Inner Term L: Last Term GP (c – 9)(c + 3) (c – 9)(c + 3) F (c)(c) O (c)(3) I (-9)(c) L (-9)(3) c2 +3c -9c-27 c2 – 6c – 27

  23. YT (2x – 5)(3x2 – 4x + 1) 2x( 3x2 – 4x + 1) -5(3x2 – 4x + 1) 6x3– 23x2+ 22x – 5 (3k + 4)(7k2+ 2k– 9) 3k( 7k2 + 2k – 9) + 4(7k2 + 2k – 9) 21k3 – 34k2– 19k– 36

  24. (n2 – 3n + 2 )(n2 + 5n – 4) YT n2(n2 + 5n – 4) – 3n(n2 + 5n – 4) + 2(n2+ 5n – 4) n4 + 2n3 – 17n2+ 22n – 8 (y2 + 7y – 1)(y2– 6y + 5) y2(y2 – 6y + 5) + 7y(y2 – 6y + 5) – 1(y2 – 6y + 5) y4+ y3– 38y2+ 41y – 5

  25. Daily Practice Study Guide Intervention Worksheet Pg. 98 1-14

  26. FOIL METHOD The length of a rectangle is 8d + 3. The width is 5d + 2. What is the Area of the Rectangle? GP F: First Term O: Outer Term I: Inner Term L: Last Term (8d + 3)(5d + 2) F (8d)(5d) O (8d)(2) I (3)(5d) L (3)(2) 40d2 + 16d +15d + 6 40d2 + 31d + 6

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