Objective The student will be able to:

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ObjectiveThe student will be able to

• Combine like terms to simplify expressions.
• Use the distributive property to simplify
  expressions.
• Simplify expressions using distributive property
  and like terms together in the same problem.

Designed by Skip Tyler, Varina High School and
Nicole Kessinger, Deep Run High School edited
by Gloria Kent, South Lenoir High School, Nov.,
2009.
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The Distributive Property

• The process of using the number on the outside of
  the parentheses with each term on the inside of
  the parentheses.
• 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)
• 5 x 5 7
• 5x 35

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Example 2 3(m - 4) 3 m - 3 4 3m - 12 Example
3 -2(y 3) -2 y (-2) 3 -2y (-6) -2y - 6
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Which statement demonstrates the distributive
property incorrectly?

1. 3(x y z) 3x 3y 3z
2. (a b) c ac bc
3. 6(3k - 4) 18k - 24
4. 5(2 3x) 10 3x

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A term is a

• 1) number,
• 2) variable, or
• 3) a product / quotient of numbers and
  variables.
• Example
• 5
• m
• 2x³

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The coefficient is

• the number attached and in front of the variable.
• Examples
• 1) 4a 4
• 2) y2
• 1

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Like Terms are terms with the same variable AND
with the same exponent.
To simplify expressions with like terms, simply
combine the like terms by adding the coefficients.
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Are these like terms? 1) 13k, 22k
Yes, the variables are the same. 2) 5ab, 4ba
Yes, the order of the variables doesnt
matter. 3) x3y, xy3 No, the exponents are on
different variables.
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Which of the following is the simplified form of
-4x 7x ?

1. -4
2. 3x
3. -3x
4. 4

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Simplify1) 5a 7a

• 12a
• 2) 6.1y - 3.2y
• 2.9y
• 3) 4x2y x2y
• 5x2y
• 4) 3m2n 10mn2 7m2n - 4mn2
• 10m2n 6mn2

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5) 13a 8a 6b

• 21a 6b
• 6) 4d 6a2 - d 12a2
• 18a2 3d

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Which of the following is the simplified form of
5x - 4 - 7x 14 ?

1. -12x 10
2. -2x 10
3. 2x - 18
4. 12x 18

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If a triangle has sides 3x - 2, 5 - x and 2x - 5,
what is the perimeter of the triangle?

1. 4x - 2
2. 4x 2
3. 5x - 2
4. 5x - 7

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Bonus! Which of the following is the simplified
form of a 3a - 4(9 - a) ?

1. -36
2. 3a - 36
3. 8a - 36
4. 8a 36