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Select the expressions that are equivalent to 7(q+4)7(q + 4).\newlineMulti-select Choices:\newline(A)(4q)7(4q)7\newline(B)11q11q\newline(C)(q+4)7(q + 4)7\newline(D)4(q+7)4(q + 7)

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Full solution

Q. Select the expressions that are equivalent to 7(q+4)7(q + 4).\newlineMulti-select Choices:\newline(A)(4q)7(4q)7\newline(B)11q11q\newline(C)(q+4)7(q + 4)7\newline(D)4(q+7)4(q + 7)
  1. Distribute 77: Distribute 77 into the parentheses: 7(q+4)=7q+287(q + 4) = 7q + 28.
  2. Compare with choices: Compare the result with each choice:\newline(A) (4q)7=28q(4q)^7 = 28q, which is not equal to 7q+287q + 28.
  3. Choice (A): (B)11q does not match 7q+28.(B) 11q \text{ does not match } 7q + 28.
  4. Choice (B): (C)(q+4)7=7(q+4)(C) (q + 4)7 = 7(q + 4), which simplifies to 7q+287q + 28, matching our expression.
  5. Choice (C): (D)4(q+7)=4q+28(D) 4(q + 7) = 4q + 28, which is not equal to 7q+287q + 28.

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