Polynomials and Algebra Tiles

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Polynomials and Algebra Tiles
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Modeling Polynomials

• Algebra tiles can be used to model expressions.
• Algebra tiles can also be used to simplify
  algebraic expressions such as polynomials.

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Modeling Polynomials

• Different shapes represent different values.
• Blue square x2
• Red square -x2

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Modeling Polynomials

• Different shapes represent different values.
• Green rectangle x.
• Red rectangle -x.

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Modeling Polynomials

• Different shapes represent different values.
• Yellow small square 1
• Red small square -1

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Modeling Polynomials

• x2
  
• x
  
• 1
  

• - x2
  
• - x
  
• - 1
  

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Zero Pairs

• The following models are called zero pairs
  because they are additive inverses of each other.
• When put together, they cancel each other out to
  model zero.

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Zero Pairs
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Modeling Polynomials

• Represent each of the following with algebra
  tiles, draw a pictorial diagram of the process,
  then write the symbolic expression.
• 2x2
• 4x
• 3

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Modeling Polynomials

• 2x2
• 4x
• 3

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Distributive Property

• 3(x2)
• Three is the quantity, so we need three groups of
  (x2)

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Distributive Property

• 3(x 2)
• 3(x) 3(2)
• 3x 6

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Distributive Property

• Represent the quantity 3(x- 4)
• 3(x 4)
• 3(x) 3(4)
• 3x 12

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Ready to Simplify

• Addition can be viewed as combining.
• Combining involves the forming and removing of
  all zero pairs.
• For each of the given examples, use algebra tiles
  to model the addition.
• Draw pictorial diagrams which show the modeling.

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Simplifying Expressions

• x 2 2x 4
• Regroup to put like terms together

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Simplifying Expressions

• Make Zero Pairs to Simplify
• New expression 3x - 2

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More Polynomials

• Represent each of the given expressions with
  algebra tiles.
• Draw a pictorial diagram of the process.
• Write the symbolic expression.
• x 4

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More Polynomials

• 2x 3
• 4x 2

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More Polynomials

• Use algebra tiles to simplify each of the given
  expressions. Combine like terms. Look for zero
  pairs. Draw a diagram to represent the process.
• Write the symbolic expression that represents
  each step.
• 2x 4 x 2
• -3x 1 x 3

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More Polynomials

• What is 2x 4 x 2?

2x 4 x 2 3x 6
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More Polynomials

• What is -3x 1 x 3?

-3x 1 x 3 -2x 4
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Simplifying Polynomials Using Algebra Tiles is
easy

• Continue to the lesson and work the practice
  problems using algebra tiles. For each problem
  sketch each polynomial and simplify each
  expression.