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**Expanding and Simplifying Algebraic Expressions**

2(x + 1) + 3(x + 3) = 2x x + 9 = 5x + 11 x + x = 2x 2x - 5x = -3x

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(x - 1)(4) Four groups of (x - 1)

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(x - 1)(4) This is a zero model.

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**How can you use algebra tiles to show that**

(x - 1)(4) = 2 + 4x The simplified expression is 2 + 4x or 4x + 2. How can you use algebra tiles to show that 2 + 4x is the same as 4x + 2 ?

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Simplify: 2x x - 5 x - 2x 3 (x - 1) -2 (x + 2)

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Simplify: x x - 5

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Simplify: 1. 2x x - 5 = 6x - 2 zero

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Simplify: 2. x - 2x

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Simplify: = -x - 6 2. x - 2x zero

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**How could you get this answer without using algebra tiles?**

Simplify: (x - 1) = 3x - 3 How could you get this answer without using algebra tiles?

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Simplify: (x - 2) Step 1 2 (x - 2) Step 2 The opposite

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**How could you get this answer without using algebra tiles?**

Simplify: (x - 2) = -2x + 4 2 (x - 2) -2 (x - 2) How could you get this answer without using algebra tiles?

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**Steps without algebra tiles**

-2 (x - 2) + 3 (2x + 1) = -2x x + 3 = 4x + 7 How could you check your answer to see if it is equivalent to the original expression?

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*Make sure all tiles are positive side up (negative [red] side down)*

*Make sure all tiles are positive side up (negative [red] side down)*

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