1. Are We Equal?? Determine whether each of the following pairs of expressions are equivalent. Some of them may not be equivalent. Be sure to justify your conclusions.

2. 6y +12 and 6(y+2) Yes, these two expressions are equivalent because of the distributive property. – The distributive property states that you can factor out a common factor between two terms being added(or subtracted). It also states that if a number is being multiplied by a sum or difference you can multiply the number by each term in the sum(or difference). So by the definition of the distributive property I can multiply the 6 times the y term and the 6 times the 2 term and get an equivalent expression of 6y+12 which is the same as the 1 st expression.

3. 3x+y and y +3x Yes these two expressions are equivalent because of the commutative property. It states that when adding terms order does not matter.

4. 3x+2 and 3(x+2) No, these expressions are not equivalent. You can discover this if you apply the distributive property to the 3(x+2) expression. By the definition of the distributive property you should multiply the 3 times the x term and the 3 times the 2 term. You would end up with an equivalent expression of 3x+6 which is not the same as 3x+2.

7. Exit Slip Which of the following expressions are equivalent? Why? If an expression has no match write two equivalent expressions to match(write the property).

8. 2(x+4) and 8+2x These two expressions are equivalent because of the distributive and the commutative property. First based on the definition of the distributive property I would multiply the 2 times the x term and the 2 times the 4 term which would simplfy to 2x +8. Then according to the commutative property when adding terms the order does not change the value, so I can just switch the 2x and 8 term and get 8+2x.

9. 2x+4  2(x+2) distributive property  4+2x commutative property 3(x+4) – (4+x)  3x+12 – (4+x) distributive property  3(4+x) – (x+4) commutative property  3(4+x) – x + 4 associative property ????  3*4+x –(x+4) associative property ???? X+4  4+x commutative property  (x+4) associative property