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Multiplying Polynomials: 3 Techniques (Distributive, FOIL, Box Method)

Learn how to multiply polynomials using the distributive property, FOIL method, and box method. Practice with various examples. Homework: Multiplying Polynomials handout.

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Multiplying Polynomials: 3 Techniques (Distributive, FOIL, Box Method)

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  1. DO NOW • Multiply the following monomials: #1.) 5xy2(4xyz) #2.) 3b6c4(7b2c2) #3.) (2m3n2)3

  2. TOPIC: Polynomials Main Idea: Multiplying Polynomials

  3. There are 3 techniques you can use for multiplying polynomials: • #1) Distributive Property • #2) FOIL • #3) Box Method

  4. DISTRIBUTIVE PROPERTY Example #1 Multiply: 2x (5x + 8y+3) Using the distributive property, 2x(5x) + 2x(8y) + 2x(3). 10x2 + 16xy + 6x Then, combine “like terms”. 10x2 + 16xy + 6x

  5. FOIL METHOD • When is the ONLY case that you can use the FOIL Method? • The FOIL method is ONLY used when you multiply 2 binomials. It is an acronym and tells you which terms to multiply.

  6. What does FOIL stand for? First terms Outer terms Inner terms Last terms

  7. Example #2: Use the FOIL method to multiply the following binomials: (y + 3)(y + 7). (y + 3)(y + 7). F tells you to multiply the FIRST terms of each binomial. y2

  8. (y + 3)(y + 7). O tells you to multiply the OUTER terms of each binomial. y2+7y

  9. (y + 3)(y + 7). I tells you to multiply the INNER terms of each binomial. y2 + 7y +3y

  10. (y + 3)(y + 7). L tells you to multiply the LAST terms of each binomial. y2 + 7y + 3y + 21 • What is your last step? • Combine like terms. y2 + 10y + 21

  11. BOX METHOD • Here is a third method of multiplying polynomials. Example #3: Multiply (3x – 5)(5x + 2) STEPS: • Draw a box. • Write a polynomial on the top and side of a box. • Multiply terms.

  12. 3) Multiply (3x - 5)(5x + 2) 15x2 First terms: Outer terms: Inner terms: Last terms: Combine like terms. 15x2 - 19x – 10 +6x -25x 15x2 -25x -10 +6x -10 You have 3 techniques. Pick the one you like the best!

  13. First terms: Outer terms: Inner terms: Last terms: Combine like terms. 21p2 – 34p + 8 Try using the BOX METHOD!Example #4: Multiply (7p - 2)(3p - 4) 21p2 -28p -6p 21p2 -6p +8 -28p +8

  14. Pick the method that works best for you!Example #5: Multiply (y + 4)(y – 3) • y2 + y – 12 • y2 – y – 12 • y2 + 7y – 12 • y2 – 7y – 12 • y2 + y + 12 • y2 – y + 12 • y2 + 7y + 12 • y2 – 7y + 12

  15. Pick the method that works best for you!Example #6: Multiply (2a – 3b)(2a + 4b) • 4a2 + 14ab – 12b2 • 4a2 – 14ab – 12b2 • 4a2 + 8ab – 6ba – 12b2 • 4a2 + 2ab – 12b2 • 4a2 – 2ab – 12b2

  16. Example #7: Multiply (2x - 5)(x2 - 5x + 4) For this example, what methods can we use? Distributive or Box Method. 2x(x2 - 5x + 4) - 5(x2 - 5x + 4) 2x3 - 10x2 + 8x - 5x2 + 25x - 20 Group and combine like terms. 2x3 - 10x2 - 5x2 + 8x + 25x - 20 2x3 - 15x2 + 33x - 20

  17. Example #7: Multiply (2x - 5)(x2 - 5x + 4) *You cannot use FOIL because they are not BOTH binomials. You must use the distributive property or box method. 2x3 -10x2 +8x Almost done! Go to the next slide! -5x2 +25x -20

  18. Example #7: Multiply (2x - 5)(x2 - 5x + 4)Combine like terms! 2x3 -10x2 +8x -5x2 +25x -20 2x3 – 15x2 + 33x - 20

  19. Example #8: Multiply (2p + 1)(p2 – 3p + 4)

  20. SUMMARY • How many methods are there for multiplying polynomials? • Which method is ONLY used for multiplying two binomials?

  21. HOMEWORK Complete “Multiplying Polynomials” Handout!

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