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Which expression is equivalent to the expression below?

7, left parenthesis, 2, y, plus, 3, right parenthesis, plus, 7, y
7(2y+3)+7y
Answer
Multiple Choice Answers
7, left parenthesis, 2, y, plus, 37, y, right parenthesis7(2y+37y)
2, y, plus, 102y+10
21, y, plus, 2121y+21
7, y, plus, 37y+3

1 answer

To simplify the expression \( 7(2y + 3) + 7y \), we will first apply the distributive property:

  1. Distribute \( 7 \) in the first part of the expression: \[ 7(2y) + 7(3) = 14y + 21 \]

  2. Now add the \( 7y \): \[ 14y + 21 + 7y \]

  3. Combine like terms: \[ (14y + 7y) + 21 = 21y + 21 \]

Now, let's look at the multiple choice answers:

  1. \( 7(2y + 37y) \) - This doesn't match our result.
  2. \( 2y + 102 \) - This also doesn't match.
  3. \( 21y + 21 \) - This matches our result.
  4. \( 7y + 37y + 3 \) - This does not match.

The expression equivalent to \( 7(2y + 3) + 7y \) is \( 21y + 21 \).