Question

3. Which two expressions are equivalent for any value of y? *
O A. 3(3y + 3) and 6y + 6
B. 3(3y + 3) and 9y + 6
O c. 9(y + 3) and 12 + 9y
O D. 9(y + 3) and 27 + 9y

Answer 1

Given:

The pair of expressions in the options.

To find:

The two expressions are equivalent for any value of y.

Solution:

Two expressions are equivalent for any value of y, iff they are equivalent.

$3(3y+3)=3(3y)+3(3)$

$3(3y+3)=9y+9$

Clearly, $3(3y+3)$ is not equivalent to $6y+6$ or $9y+6$. So, options A and B are incorrect.

$9(y+3)=9(y)+9(3)$

$9(y+3)=9y+27$

$9(y+3)=27+9y$

The expression $9(y+3)$ is not equivalent to $12+9y$. So, option C is incorrect.

The expression $9(y+3)$ is equivalent to $27+9y$.

Therefore, the correct option is D.