Which expression is equivalent to 3(–7d + 1)

To find the expression equivalent to ( 3(–7d + 1) ), we can distribute the 3 to both terms inside the parentheses.

1. Distribute:

[

3 times (–7d) + 3 times 1 = –21d + 3

]

Now, we will compare ( –21d + 3 ) with the given options:

1. ( 1(3d – 7) = 3d – 7 ) (not equivalent)
2. ( (–7d + 1)3 = –21d + 3 ) (this matches!)
3. ( 3(d – 7) = 3d – 21 ) (not equivalent)
4. ( –7(3d + 1) = –21d – 7 ) (not equivalent)

Thus, the expression equivalent to ( 3(–7d + 1) ) is ( (–7d + 1)3 ).