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The Distributive Property and Like Terms

This review covers the distributive property and like terms in expressions, including how to combine like terms and how to use the distributive property to simplify expressions.

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The Distributive Property and Like Terms

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  1. The Distributive Property and Like Terms

  2. Review 4 is the coefficient of x 3 is the coefficient of

  3. LIKE Terms Like terms are terms in an expression that have the - same variable - raised to the same power

  4. LIKE Terms 5x and 3x are like terms 4 and 2 are also like terms 7x2 and x2 are also like terms

  5. LIKE Terms 5x and 7x2 are NOT like terms WHY????

  6. LIKE TERMS 3b and 5b 7x2 and 5x2 14c and 8c 7c3 and 5c3 NOT like terms 3b and 5c 7x2 and 7y2 12x2 and 7x 18a and 18b LIKE TERMS same variable raised to the same power

  7. Like Terms?? 8a and 12a 7a and 7b 8x2 and 12x2 12g and g2 c and 8c 18b5 and 2b2 5ab and 7bc 7c3 and 5c3 8b and 5c 5c2 and 7c2 3x2 and 7z2 10x2 and 8x2 5xy and 6x 18a and 18b 5a and 8a 8x3 and 12c3

  8. What do we do with LIKE TERMS? We can add the coefficients together. (We can subtract also) Be careful - the coefficient changes but the variable and power do NOT change.

  9. Combine Like Terms 8a + 12a = 20a 8x2 + 12x2 = 20x2 c + 8c = 9c 18b5 - 2b5 = 16b5 5b + 7b = 12b 7c3 + 5c3 = 12c3 coefficient changes the variable and power do NOT change.

  10. Combine Like Terms 5c2 + 7c2= 12c2 10z2 + 8z2 = 18z2 5y + 6y = 11y 5a + 8a = 13a 10x3 – 3x3= 7x3 a + 6a = 7a coefficient changes the variable and power do NOT change.

  11. Combine Like Terms 8a + a = 8x2 + 6x2 = 5c + 12c = 18x5 – 2x5 = 15w - 7w = 9c3 + 3c3 = coefficient changes the variable and power do NOT change.

  12. Combine Like Terms 5y2 + 7y2= 2r2 + 3r2 = 8y - y = 11a + 8a = 12x3 – 5x3= 12a + a = coefficient changes the variable and power do NOT change.

  13. The Distributive Property The product of 4 and (2+3x): 4(2+3x) 4●2 + 4 ● 3x 8 + 12x Sharing what is Outsidethe parentheses with EVERYTHING INSIDE the parentheses.

  14. Example using the distributive property

  15. Example using the distributive property

  16. The Distributive Property The product of 5 and (a + 12): 5(a + 12) 5●a + 5 ● 12 5a + 60 Sharing what is Outsidethe parentheses with EVERYTHING INSIDE the parentheses.

  17. Example using the distributive property

  18. Another Example

  19. Another Example

  20. Another Example

  21. Another Example

  22. Another Example

  23. Simplify

  24. Simplify

  25. Simplify

  26. Simplify

  27. Simplify

  28. Another Example

  29. Simplify

  30. Another Example

  31. Simplify

  32. Simplify

  33. Simplify

  34. Simplify

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