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Combining Like Terms

Combining Like Terms. Simplify Expression. Simplify: Combine like terms 3 dogs + 3 cats + 5 dogs = 3d + 5c + 6d = Like terms- because they both have d as a variable (Just add the coefficients # and keep the variable(s) the same). 8 dogs + 3 cats. 9d + 5c. Simplify Each Expression.

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Combining Like Terms

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  1. Combining Like Terms

  2. Simplify Expression • Simplify: Combine like terms • 3 dogs + 3 cats + 5 dogs = • 3d + 5c + 6d = • Like terms- because they both have d as a variable (Just add the coefficients # and keep the variable(s) the same) 8 dogs + 3 cats 9d + 5c

  3. Simplify Each Expression 3x + 2x = 5x 8y – 2y + 5 = 6y + 5 8y – 2y = 6y 4k + 17 - 2k = 2k + 17 4k – 2k = 2k Watch the sign in front of the number!!!!

  4. Simplify Each Expression 3xy + 2xy = 5xy 3x +8y – 2y + 5 = 3x + 6y + 5 8y – 2y = 6y 6k -3k + 10 + 4k = 7k + 10 6k – 3k + 4k = 7k Watch the sign in front of the number!!!!

  5. Simply Each Expression • Simplify the expression 6x + 5y² - y²= If there is no # in front of a variable it is a understood 1 1 4y² + 6x 5y² - 1y² = 4y² 4y + 23 – y – 6 = 1 3y + 17 4y -1y = 3y 23 - 6 = 17 8p - 5p + 5 – p – 2 = 1 2p + 3 8p – 5p -1p = 2p 5 -2 = 3

  6. Simplify Each Expression 2b – 8 + 4b – 6b -19 – 11a + a + 16 1 2b + 4b – 6b = 0b -19 + 16 = - 3 -8 -11a + a = -10a -10a - 3 b – 9b= -8b If there is no # in front of a variable it is a understood 1

  7. Simplify the expression A) Simplify the expression • 6x + 5y² - y²= 4y² + 6x 1 5y² - 1y² = 4y² B) Evaluate your answer for the given values 4y² + 6x X = 5, y = 3 4(3)² + 6 (5) 4(9) + 6(5) 36 + 30 = 66

  8. Simplify the expression A) Simplify the expression 5bc + 3c² + c²= 1 5bc + 4c² 3c² + 1c² = 4c² B) Evaluate your answer for the given values 5bc + 4c² b = 3, c = 2 5(3)(2) + 4(2)² 15(2) + 4(4) 30 + 16 = 46

  9. Simplifying with Distributive Property Distributive Property: multiplying coefficient by what’s inside ( )’s to simplify Example 3(5+6) Distributive Property: Means to share the outside number with everything on the inside by multiplying 3 x 5 = 15 3 x 6 = 18 15 + 18 = 33 3(2x + 3) 3 x 2x = 6x 3 x 3 = 9 6x + 9

  10. Simplifying with Distributive Property 3(2x + 4x²) + 5 (2x² + 5x) 3 ( 2x)= 6x + 5 ( 2x²)= 10x² 3 ( 4x²)= 12x² + 5 (5x) = 25x 6x + 12x²+ 10x² + 25x = 22x² + 31x Distributive Property: Means to share the outside number with everything on the inside by multiplying

  11. Simplifying with Distributive Property -2 (2m -1) + 4m 4(d + 3) + 7d Don’t forget a negative times a negative makes a positive 4(d) + 4(3) 4d + 12 + 7d -2 (2m) -2(-1) -4m + 2 + 4m 4d + 7d = 11d - 4m + 4m = 0m 11d + 12 2 Distributive Property: Means to share the outside number with everything on the inside by multiplying

  12. Simplifying with Distributive Property -2 (2m -1) + 4m 4(d + 3) + 7d Don’t forget a negative times a negative makes a positive 4(d) + 4(3) 4d + 12 + 7d -2 (2m) -2(-1) -4m + 2 + 4m 4d + 7d = 11d - 4m + 4m = 0m 11d + 12 2 Distributive Property: Means to share the outside number with everything on the inside by multiplying

  13. Simplifying 7d - 3 = 3d +1 7d -3 (+3) = 3d + 1 (+3) 7d = 3d +4 7d (-3d) = 4 4d = 4 d = 1

  14. Simplifying 8c - 2 = 2c +10 8c -2 (+2) = 2c + 10 (+2) 8c = 2c +12 8c (-2c) = 12 6c = 12 c=2

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