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2.7 The Distributive Property

Learn how to simplify expressions by using the distributive property and factoring. Combine like terms and factor out the greatest common factor to simplify expressions easily.

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2.7 The Distributive Property

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  1. 2.7 The Distributive Property

  2. Simplify by using the Distributive Property 6 ( 3x + 5 ) 6 ● 3x = + 6 ● 5 = 18x + 30

  3. Simplify by using the Distributive Property 5 ( 2 + 7y ) 5 ● 2 = + 5 ● 7y = + 35y 10 = 35y + 10

  4. Simplify by using the Distributive Property -4 ( 8a - 9 )

  5. Simplify by using the Distributive Property -5(x – 3y +8z)

  6. Simplify by using the Distributive Property 4( s – t + w ) 3

  7. Simplify by using the Distributive Property 5( x – 3y + 8z) 6

  8. Factoring • The reverse of multiplying • Factor out the greatest common factor (GCF) of all terms

  9. Factor 5 x + 5 y = 5(x + y)

  10. Factor 9x + 27y = 9x + 9 (3y) = 9 (x + 3y)

  11. Factor 18a + 21b = 3(6a) + 3(7b) = 3 (6a + 7b)

  12. Factor 5x – 35y – 10

  13. Try on your own…Factor - 25y + 15w + 5

  14. What is a term? • Terms are separated by addition or subtraction What are these terms called? x - 15 + 8y coefficient Variable term Variable Term Constant Term

  15. What are “like terms”? same VARIABLE and same EXPONENT 2x + 5x 27 - 6z NOT LIKE TERMS LIKE TERMS

  16. What are “like terms”? same VARIABLE and same EXPONENT 3m + m - 20m w²+ w NOT LIKE TERMS LIKE TERMS

  17. Combine like terms 5x + 4x + 2x add coefficients = 11x

  18. Combining Like Terms • Change all subtraction to adding the opposite. • Combine like terms. 5x - (-9) + 2x + 7 = 5x + 9 + 2x + 7 = 7x + 16

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