Which expression is equivalent to 4(2 + y)?

Which expression is equivalent to 4(2 + y)?

• A. 8 + y
• B. 8 + 4y
• C. 8y
• D. 4y + 2

Answer: (B)

The expression uses the distributive property: when you multiply a number outside the parentheses by a sum, you multiply it by each term inside and add the results. So 4(2 + y) is 4×2 plus 4×y, which gives 8 + 4y. That matches the option with an 8 and a 4y term, and is the correct equivalent expression. The other forms don’t match for all values of y. For example, eight plus y would only be correct if the 4 was not applied to y, which isn’t the case here. Eight y would be missing the constant 8, and 4y plus 2 would have 2 instead of 8.

The expression uses the distributive property: when you multiply a number outside the parentheses by a sum, you multiply it by each term inside and add the results. So 4(2 + y) is 4×2 plus 4×y, which gives 8 + 4y. That matches the option with an 8 and a 4y term, and is the correct equivalent expression.

The other forms don’t match for all values of y. For example, eight plus y would only be correct if the 4 was not applied to y, which isn’t the case here. Eight y would be missing the constant 8, and 4y plus 2 would have 2 instead of 8.