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.