Distributive Property

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Distributive Property and Combining Like Terms
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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)
• 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. 5(2 3x) 10 3x
4. 6(3k - 4) 18k - 24

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A term is a

• 1) number,
• 2) variable, or
• 3) a product / quotient of numbers and
  variables.
• Example
• 5
• m
• 2x2

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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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The coefficient is

• the numerical part of the term.
• Examples
• 1) 4a
• 4
• 2) y2
• 1

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Like Terms are terms with the same variable AND
exponent.
To simplify expressions with like terms, simply
combine the like terms.
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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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(No Transcript)
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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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Which figure below models the simplification of -
4x - 5 7x 7 using these tiles?

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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