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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(x+2) Three is the quantity, so we need three groups of (x+2)

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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 x – 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 x + 2 -3x x + 3

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More Polynomials What is 2x x + 2? 2x x + 2 = 3x + 6

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More Polynomials What is -3x x + 3? -3x 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.

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