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Are We Equal??

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. 6y +12 and 6(y+2). Yes, these two expressions are equivalent because of the distributive property.

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Are We Equal??

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  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 1st 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.

  5. Yes, according to the distributive property these two expressions are equivalent. By definition you can factor out a 5 from each term in the 1st expression() leaving you with 5() + 5(3). Which you can then change to , which is the same as the second expression.

  6. Yes, by the definition of the distributive property these two expressions are equivalent. You can generate the 1st expression from the second by using the distributive property and multiplying the 3 times the term and the 3 times the .

  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

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