Distribution and Like Terms

Learn how to use algebra tiles to visualize distribution and combining like terms in algebraic expressions. Explore examples like simplifying expressions by identifying like terms, distributing terms, and combining coefficients effectively.

• Algebra Tiles
• Distribution
• Like Terms
• Simplifying Expressions
• Algebraic Manipulation

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Uploaded on Feb 19, 2025 | 0 Views

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Presentation Transcript

1. Distribution and like terms A look at the algebra behind algebra tiles .

2. Combining like terms When combining like terms, add the coefficients on each group of like terms. Example 1: 6x + 5 + 2x With algebra tiles With algebra Identify like terms. 6x + 5 + 2x 6x + 5 + 2x Add the coefficients on like terms. (6 + 2)x + 5 8x + 5 Simplify. 8 positive x-bars and 5 positive units 8x + 5

3. Example 2: 9x + 4 2x 9x + 4 + -2x With algebra tiles 9x + 4 2x Algebraically Identify like terms. 9x + 4 2x Combine the coefficients on like terms. (9 + -2)x + 4 7x + 4 Simplify. 7 positive x-bars and 4 positive units 7x + 4

4. Example 3: 6x + 5 + -3x + -8 With algebra tiles 6x + 5 + -3x + -8 Algebraically Identify like terms. 6x + 5 + -3x + -8 Add the coefficients on like terms. (6 + -3)x + (5 + -8) 3x + -3 3x 3 Simplify. 3 positive x-bars and 3 negative units 3x + -3 3x 3

5. Distribution Multiply the term outside the parentheses by each term inside the parentheses. Example 4: 3(x + 5) With algebra tiles Algebraically 3(x + 5) 3(x + 5) Distribute. Build 3 groups of 1x + 5. 3(x) + 3(5) Multiply. 3x + 15 Simplify. 3 positive x-bars and 15 positive units 3x + 15

6. Example 5: 2(3x 1) With algebra tiles 2(3x + -1) Algebraically Build 2 groups of 3x + -1. 2(3x + -1) Distribute. 2(3x) + 2(-1) Multiply. 6x + -2 6x 2 Simplify. 6 positive x-bars and 2 negative units 6x + -2 = 6x 2

7. Example 6: 2(x2 2x + 1) With algebra tiles 2(x2 + -2x + 1) Algebraically Build 2 groups of x2 + -2x + 1. 2(x2 + -2x + 1) Distribute. 2(x2) + 2(-2x) + 2(1) Multiply. 2x2 + -4x + 2 2x2 4x + 2 Simplify. 2 positive x2 tiles, 4 negative x-bars, and 2 positive units 2x2 + -4x + 2 = 2x2 4x + 2

8. Distribution and combining like terms Example 7: 4(2x + 5) 8 4(2x + 5) + -8 Distribution first. 4(2x) + 4(5) + -8 8x + 20 + -8 Identify like terms. Combine like terms. 8x + (20 + -8) 8x + 12 Simplify.

9. Example 8: -4 + 5(2x + 3) + x -4 + 5(2x + 3) + x Distribution first. -4 + 5(2x) + 5(3) + 1x -4 + 10x + 15 + 1x Identify like terms. (10 + 1)x + (-4 + 15) Combine like terms. 11x + 11 Simplify.