Q. Which pair of expressions below are equivalent?y+z+z+z and 4yz7(6y−3) and 42y−37(6y−3) and 42y−217(6y) and 13y
Combine Like Terms: Compare the first pair of expressions y+z+z+z and 4yz.Simplify y+z+z+z by combining like terms.y+z+z+z=y+3zCheck if this is equivalent to 4yz.y+3z is not equivalent to 4yz because the terms are not similar and cannot be factored or simplified to make the expressions look the same.
Distribute and Compare: Compare the second pair of expressions 7(6y−3) and 42y−3. Distribute the 7 in the expression 7(6y−3). 7(6y−3)=42y−21 Check if this is equivalent to 42y−3. 42y−21 is not equivalent to 42y−3 because the constants are different (−21 vs. −3).
Check Equivalence: Compare the third pair of expressions 7(6y−3) and 42y−21. Distribute the 7 in the expression 7(6y−3) again. 7(6y−3)=42y−21 Check if this is equivalent to 42y−21. 42y−21 is equivalent to 42y−21 because both expressions are identical after the distribution.
Distribute and Compare: Compare the fourth pair of expressions 7(6y) and 13y. Distribute the 7 in the expression 7(6y). 7(6y)=42y Check if this is equivalent to 13y. 42y is not equivalent to 13y because the coefficients are different (42 vs. 13).
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