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Which pair of expressions below are equivalent?

y+z+z+z and 
4yz

7(6y-3) and 
42 y-3

7(6y-3) and 
42 y-21

7(6y) and 
13 y

Which pair of expressions below are equivalent?\newliney+z+z+z y+z+z+z and 4yz 4 y z \newline7(6y3) 7(6 y-3) and 42y3 42 y-3 \newline7(6y3) 7(6 y-3) and 42y21 42 y-21 \newline7(6y) 7(6 y) and 13y 13 y

Full solution

Q. Which pair of expressions below are equivalent?\newliney+z+z+z y+z+z+z and 4yz 4 y z \newline7(6y3) 7(6 y-3) and 42y3 42 y-3 \newline7(6y3) 7(6 y-3) and 42y21 42 y-21 \newline7(6y) 7(6 y) and 13y 13 y
  1. Combine Like Terms: Compare the first pair of expressions y+z+z+zy+z+z+z and 4yz4yz.\newlineSimplify y+z+z+zy+z+z+z by combining like terms.\newliney+z+z+z=y+3zy + z + z + z = y + 3z\newlineCheck if this is equivalent to 4yz4yz.\newliney+3zy + 3z is not equivalent to 4yz4yz because the terms are not similar and cannot be factored or simplified to make the expressions look the same.
  2. Distribute and Compare: Compare the second pair of expressions 7(6y3)7(6y-3) and 42y342y-3. Distribute the 77 in the expression 7(6y3)7(6y-3). 7(6y3)=42y217(6y-3) = 42y - 21 Check if this is equivalent to 42y342y-3. 42y2142y - 21 is not equivalent to 42y342y-3 because the constants are different (21-21 vs. 3-3).
  3. Check Equivalence: Compare the third pair of expressions 7(6y3)7(6y-3) and 42y2142y-21. Distribute the 77 in the expression 7(6y3)7(6y-3) again. 7(6y3)=42y217(6y-3) = 42y - 21 Check if this is equivalent to 42y2142y-21. 42y2142y - 21 is equivalent to 42y2142y-21 because both expressions are identical after the distribution.
  4. Distribute and Compare: Compare the fourth pair of expressions 7(6y)7(6y) and 13y13y. Distribute the 77 in the expression 7(6y)7(6y). 7(6y)=42y7(6y) = 42y Check if this is equivalent to 13y13y. 42y42y is not equivalent to 13y13y because the coefficients are different (4242 vs. 1313).

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