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Like Terms are terms with the same variable AND exponent.

This tutorial explains how to simplify expressions with like terms, combine variables with the same exponents, and apply the distributive property. Examples and interactive exercises included.

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Like Terms are terms with the same variable AND exponent.

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  1. Like Termsare terms with the same variable AND exponent. To simplify expressions with like terms, simply combine the like terms.

  2. Are these like terms? 1) 13k, 22k Yes, the variables are the same. 2) 5ab, 4ba Yes, the order of the variables doesn’t matter. 3) x3y, xy3 No, the exponents are on different variables.

  3. 2) 6.1y - 3.2 3) 4x2y + 6ab 4) 3m2n + 10mn2 Here you DO NOTHING1) 5a + 7

  4. Answer Now Which of the following is the simplified form of -4x + 7x ? • -4 • 3x • -3x • 4

  5. are like terms and 5a and a are like terms The above expression simplifies to:

  6. Answer Now Which of the following is the simplified form of 5x - 4 - 7x + 14 ? • -12x + 10 • -2x + 10 • 2x - 18 • 12x – 18

  7. Here you have to Simplify1) 5a + 7a 2) 6.1y - 3.2y 3) 4x2y + x2y 4) 3m2n + 10mn2 + 7m2n - 4mn2

  8. The Distributive Property The process of distributing the number on the outside of the parentheses to each term on the inside. a(b + c) = ab + ac and (b + c) a = ba + ca a(b - c) = ab - ac and (b - c) a = ba - ca Example #1 5(x + 7) 5x + 35

  9. Example #2 3(m - 4) 3m - 12 Example #3 -2(y + 3) -2y - 6

  10. 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

  11. 2) 6.1(y - 3.2) 3) (4x+y)(-5) 4) 2(3m + 10 + 7n) Here you have to Distribute!1) 5(a + 7)

  12. Will you Simplify, Distribute, or Do Nothing? 2x + 3y - x Combine Like Terms 17x + 4y Do Nothing 2(4x + 3) Distribute (-2y + 6)(-5) Distribute 11ab – 3b Do Nothing 2x + 3(4x – 1) BOTH Combine Like Terms and Distribute!

  13. Don’t Get Bit! First, decide if you should Simplify, Distribute, or Do Nothing. Then do the problem. 13a + 8a + 6b 21a + 6b Combine Like Terms 18a2 + 3d 4d + 6a2 - d + 12a2 Combine Like Terms -42x + 54 (7x – 9)(-6) Distribute

  14. Answer Now Bonus! Which of the following is the simplified form of a + 3a - 4(9 - a) ? • -36 • 3a - 36 • 8a - 36 • 8a + 36

  15. Distribution Game • http://www.hstutorials.net/dialup/distributiveProp.htm

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