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Distribution and like terms

Distribution and like terms. A look at the algebra behind algebra tiles…. 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. 6x + 5 + 2x. Identify like terms.

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Distribution and like terms

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  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 6x + 5 + 2x Identify like terms. 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. 8x + (20 + -8) Combine like terms. 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.

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