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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