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Distributive Law for Polynomials

Distributive Law for Polynomials. Let’s have some fun!. Plan for the Period:. Brief Review on Board Split into Teams to practice Playoff w/ prizes for winning team. Monomial * Monomial. 18x 42m 2 x 3 y. 3 * 6x = 6m * 7m = x 2 * xy =

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Distributive Law for Polynomials

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  1. Distributive Lawfor Polynomials Let’s have some fun!

  2. Plan for the Period: • Brief Review on Board • Split into Teams to practice • Playoff w/ prizes for winning team

  3. Monomial * Monomial • 18x • 42m2 • x3y • 3 * 6x = • 6m * 7m = • x2 * xy = • Suppose a school has s students, and each one brings in 3 CD’s to school. If each CD case is a square with side d cm, how much area would all the CD’s take if placed on the gym floor? • s * 3 * d * d = 3sd2 cm2

  4. Monomial * Binomial • 6x * (x2 + 4) (using term by term method) • 6x * x2 + 6x * 4 = • 6x * (x2 + 4) (using Napier’s Bones) x2 +46x 6x3 + 24x

  5. Binomial * Binomial • (x-1) * (-2x + 3) (using term by term method) x*(-2x) + x*(3) • (x-1) * (-2x2 + 3) (using Napier’s Bones) -2x +3 x -1 -1 * (-2x) -1 * (3) = -2x2+3x+2x-3 = -2x2+5x-3 -2x2 5x -3 Note: Be sure that each diagonal has same degree!

  6. Team Practice Time • I will call out the teams, please sit quietly until all teams have been called. • Teams will then work on practice sheets in preparation for the playoff. • Be sure all team members know how to multiply 2 binomials.

  7. Playoff Rules • Each team member has a unique color pen. No swapping! • Each round, 2 members from team will have special roles: • One is at the Buzzer • One is the scribe • The scribe has to write the problem and the group’s solution on the whiteboard in their color pen. • Group hands whiteboard to member at Buzzer, who can then hit buzzer. (No early buzzering!!!!) • Buzzer teammate has 10 seconds to review answer from team and possibly change it. NOTE: All answers must be in decreasing order of degree! (example: 6x2 +1 instead of 1 + 6x2) • If Buzzer gives correct answer, team gets 2 points. All groups that get correct answer will get 1 point. The judge’s decision is final! Arguing will mean 0 points!

  8. Question 1 • Buzzer – red • Scribe – black • 4x * (x + 1) • Answer: 4x2 + 4x

  9. Question 2 • Buzzer – black • Scribe – blue • 3x * (2 - x) • Answer: -3x2 + 6x

  10. Question 3 • Buzzer – blue • Scribe – red • -x * (-x – 1) • Answer: x2 + x

  11. Question 4 • Buzzer – black • Scribe – red • (x+1) * (x - 1) • Answer: x2 + 1

  12. Question 5 • Buzzer – blue • Scribe – black • (x+3) * (x - 3) • Answer: x2 - 9

  13. Question 6 • Buzzer – red • Scribe – blue • (2x-1) * (4-x) • Answer: -2x2+9x-4

  14. Reflection • Create your own problem in which 2 binomials are multiplied together, and solve it. • Reflection: Which method of applying the distributive property do you like better when multiplying polynomials, term-by-term or Napier’s Bones? Why?

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