Distributive Law for Polynomials

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Distributive Lawfor Polynomials

• Lets 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

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

• 18x
• 42m2
• x3y

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Monomial Binomial

• 6x (x2 4) (using term by term method)
• 6x x2 6x 4
• 6x (x2 4) (using Napiers Bones)
  x2 46x

6x3 24x
6x3 24x

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Binomial Binomial

• (x-1) (-2x 3) (using term by term
  method)
• x(-2x) x(3)
• (x-1) (-2x2 3) (using Napiers Bones)
  -2x 3
  x -1

-1 (-2x) -1 (3)
-2x23x2x-3
-2x25x-3


-2x2 3x
2x -3
-2x2 5x -3 Note Be sure
that each diagonal has same degree!
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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.

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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
  groups 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 judges decision is final!
  Arguing will mean 0 points!

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Question 1

• Buzzer red
• Scribe black
• 4x (x 1)
• Answer 4x2 4x

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Question 2

• Buzzer black
• Scribe blue
• 3x (2 - x)
• Answer -3x2 6x

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Question 3

• Buzzer blue
• Scribe red
• -x (-x 1)
• Answer x2 x

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Question 4

• Buzzer black
• Scribe red
• (x1) (x - 1)
• Answer x2 1

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Question 5

• Buzzer blue
• Scribe black
• (x3) (x - 3)
• Answer x2 - 9

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Question 6

• Buzzer red
• Scribe blue
• (2x-1) (4-x)
• Answer -2x29x-4

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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 Napiers
  Bones? Why?