Notes 3-1 The Distributive Property



Algebra I Name ___________________________

2.5 - The Distributive Property Date _______________ Block _______

KEY VOCABULARY

___________________ _______________________ are expressions that have the same value for all values of the variables.

Ex. 3(x + 2) = 3x + 3(2)

The distributive property is used to find the ___________________ of a number and a

___________ or ______________________ .

|The Distributive Property |

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|Algebra Examples |

|a(b + c) = ab + ac 3(4 + 2) = 3( ___ ) + 3( ___ ) |

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|(b + c)a = ba + ca (3 + 5)2 = ___(2) + ___(2) |

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|a(b – c) = ab – ac 5(6 – 4) = ___( ___ ) - ___( ___ ) |

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|(b – c)a = ba – ca (8 – 6)4 = ___( ___ ) - ___( ___ ) |

Examples

1. 3(x + 2) = 2. 2(r – 4) = 3. (n + 6)n

3(___) + 3(___) 2(___) – 2(___) ___(___) + ___(___)

____________ ____________ _______________

Your Turn

|1. 2(x + 3) |2. (2 – n)8 |3. 4(y + 2) |

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|4. 6(4 – x) |5. n(n – 9) |6. 3m(m – 5) |

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DISTRIBUTING A NEGATIVE can be TRICKY! Follow the same steps shown earlier;

just BE CAREFUL WITH YOUR NEGATIVES!

Examples

4. -2(x + 7) =

= (___)(x) + (___)(7) Distribute _____ .

= ______ + ______ Simplify.

= ______________ Rewrite “add the opposite” as __________ .

5. (5 - y)(-3y) =

= (___)(-3y) - (___)(-3y) Distribute _____ .

= ______ - ______ Simplify.

= ______________ Rewrite “add the opposite” as __________ .

6. -(2x - 11) =

= (___)(2x) - (___)(11) Distribute _____ .

= ______ - ______ Simplify.

= ______________ Rewrite “add the opposite” as __________ .

Your Turn

|7. -5(n + 4) |8. –(4 – y) |9. (m – 5)(-3m) |

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|10. –a(3 + a) |11. –(2x – 11) |12. [pic] |

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Distribute BEFORE combining like terms.

Examples

1. 2(6x – 4) + x = _____(6x) – ___ (4) + x Distribute _________ .

= _______ - _____ + x Simplify.

= __________________ Combine like terms.

2. -2(m + 5) – 4x = (____)(m) + (____)(5) – 4x Distribute _________ .

= ________ + _______ - 4x Simplify.

= ____________________ Combine like terms.

= ____________________ Rewrite as __________.

3. x – 3(x – 4) = ____________________ Distribute __________ .

= ____________________ Simplify.

= ____________________ Combine like terms.

Your Turn

|1. 2(4a + 1) + a |2. 3(2 – c) – c |3. 6r + (r + 4)2 |

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|4. 15t – (t – 4) |5. -6(v + 1) + v |6. 6(5 – z) + 2z |

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