Decide upon your answer and then check the "Explanation" drop down. 
1. Explain why the following statements are equivalent: 4(x + y) = 4x + 4y



2. Rewrite this expression using the Distributive Property: 6x + 12



3. Using the Distributive Property, write an expression equivalent to 5(x  6).



4. Rewrite this expression using the Distributive Property: 5x  25



5. Explain why the following statements are equivalent: a + (b + 4) = a + (4 + b)



6. Using the Commutative Property, write an equivalent expression for 5•(7x).



7. Explain why the following equation is true: (x + 4) + (x + ( 4)) = 0.



8. Simplify this expression and justify your steps: 12 + 3(a + 2b)  2a  3b  9 + b


(The Explanation shown below is one possible solution.)

• 
12 + 3(a + 2b)  2a  3b  9 + b 

• 
12 + 3a + 6b  2a  3b  9 + b 

• 
12  9 + 3a  2a + 6b  3b + b 

• 
(12  9) + (3a  2a) + (6b  3b + b) 

• 
(3) + (3a  2a) + (6b  3b + b) 

• 
3 + a(3  2) + b(6  3+ 1) 

• 
3 + a(1) + b(4) 

• 
3 + a + 4b 
