Select the expressions that are equivalent to 4(2p+7).

1) 28p+8
2) 8p+28
3) (7+2p)4
4) 2p+28

1 answer

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:

  1. \( 28p + 8 \)
    This is not equivalent to \( 8p + 28 \).

  2. \( 8p + 28 \)
    This matches our simplified expression!

  3. \( (7+2p)4 \)
    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!

  4. \( 2p + 28 \)
    This is not equivalent to \( 8p + 28 \).

Thus, the expressions that are equivalent to \( 4(2p+7) \) are:

  • 2) \( 8p + 28 \)
  • 3) \( (7 + 2p)4 \)