CC1_PG_Ch2_3.pdf - DISTRIBUTIVE PROPERTY 2.3.3 and 2.3.4...

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DISTRIBUTIVE PROPERTY 2.3.3 and 2.3.4
The Distributive Property shows how to express sums and products in two ways:
a ( b + c ) = ab + ac . This can also be written ( b + c ) a = ab + ac .
Factored form Distributed form Simplified form
a ( b + c ) a ( b ) + a ( c ) ab + ac
To simplify: Multiply each term on the inside of the parentheses by the term on the outside.
Combine terms if possible.
For additional information, see the Math Notes boxes in Lessons 2.3.4 and 7.3.2 of the Core
Connections, Course 1 text. For additional examples and practice, see the Core Connections,
Course 1 Checkpoint 8A materials.
Example 1 Example 2 Example 3
2(47) = 2(40 + 7)
= (2 ⋅ 40) + (2 ⋅ 7)
= 80 + 14 = 94
3( x + 4) = (3 ⋅ x ) + (3 ⋅ 4)
= 3 x + 12
4( x + 3 y + 1) = (4 ⋅ x ) + (4 ⋅ 3 y ) + 4(1)
= 4 x + 12 y + 4
Problems
Simplify each expression below by applying the Distributive Property.
1. 6(9 + 4) 2. 4(9 + 8) 3. 7(8 + 6) 4. 5(7 + 4)
5. 3(27) = 3(20 + 7) 6. 6(46) = 6(40 + 6) 7. 8(43) 8. 6(78)
9. 3( x + 6) 10. 5( x + 7) 11. 8( x – 4) 12. 6( x – 10)
13. (8 + x )4 14. (2 + x )5 15. –7( x + 1) 16. –4( y + 3)
17. –3( y – 5) 18. –5( b – 4) 19. –( x + 6) 20.