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Distributive Property and Simplifying Expressions

Learn how to use the distributive property to simplify expressions and interpret terms, coefficients, and factors.

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Distributive Property and Simplifying Expressions

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  1. 1. m - 10 = 15 5 2. z + 2 = 26 6 3. 3a - 8 = 4 *You MUST show all your steps mathematically, but you do not have to write out your steps in words Warm-up

  2. Distributive Property Week 1 Day 3 January 8th, 2014

  3. Essential Question: How do we use the distributive property to simplify expressions? A.SSE.1 Interpret expressions that represent a quantity in terms of its context. • Interpret parts of an expression, such as terms, factors, and coefficients. • Interpret complicated expressions by viewing one or more of their parts as a single entity. Standards:

  4. Vocabulary • The Distributive Property • Term • Coefficient • Factor

  5. The Distributive Property The process of distributing the number on the outside of the parentheses to each term on the inside. Example 5(x + 7) 5 • x + 5 • 7 5x + 35

  6. Examples 1. 5(2x+1) = 5(2x) + 5(1) = 10x + 5 2. -3(x +5) = -3(x) + -3(5) = -3x – 15 3. 2 –3(x + 6) = 2 - 3(x) + -3(6) = 2 – 3x – 18 = -3x – 16

  7. Answer Now Which statement demonstrates the distributive property incorrectly? • 3(x + y + z) = 3x + 3y + 3z • (a + b) c = ac + bc • 5(2 + 3x) = 10 + 3x • 6(3k - 4) = 18k - 24

  8. A term is a 1) number, 2) variable, or 3) a product / quotient of numbers and variables. Example 5 m 2x2

  9. 3) The coefficient is the numerical part of the term. Examples 1) 4a 4 2) y2 1

  10. Factor Factors are numbers you can multiply together to get another number: EX. 2 and 3 are factors of 6, because 2x3=6 In Algebra, factors are what you can multiply together to get an expression.

  11. Try the following on your own 1. 4 + 6(3 – x) 2. -2(x + 4) +3 3. 2(x + 6 – 3)

  12. 1. 4 + 6(3 - x) 2. -2(x+4)+3 = 4+ 6(3) - 6(x) = 4 + 18 - 6x = 22 - 6x = -2(x) + -2(4)+3 = -2x + -8 +3 = -2x – 5 3. 2(x+ 6 – 3) = 2(x) + 2(6) – 2(3) = 2x + 12 – 6 = 2x + 6

  13. Homework • 2x + 3(6x - 12) = 124 • 3x + 5(2x - 9) = 98 • 6x + 2(5x + 5) = 122

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