To determine which expressions are equivalent to \( 4(2p+7) \), we will simplify the expression first.
Starting with \( 4(2p+7) \): \[ 4(2p+7) = 4 \cdot 2p + 4 \cdot 7 = 8p + 28 \]
Now, let's evaluate each of the provided options:
-
\( 28p + 8 \)
This is not equivalent to \( 8p + 28 \). -
\( 8p + 28 \)
This matches our simplified expression! -
\( (7+2p)4 \)
This can be simplified as follows: \[ (7 + 2p)(4) = 4 \cdot 7 + 4 \cdot 2p = 28 + 8p = 8p + 28 \] This matches our simplified expression as well! -
\( 2p + 28 \)
This is not equivalent to \( 8p + 28 \).
Thus, the expressions that are equivalent to \( 4(2p+7) \) are:
- 2) \( 8p + 28 \)
- 3) \( (7 + 2p)4 \)