Question

select the correct answer.

which algebraic equation correctly represents this statement?

the square of the product of 4 and a number is the sum of the number and 15.

\\((4x)^2 = x + 15x\\)

\\(4x^2 = x + 15\\)

\\(2(4x) = x + 15\\)

\\((4x)^2 = x + 15\\)

Explanation:

Define the variable

Let the unknown number be represented by \(x\).

Translate the verbal phrases

• "The product of 4 and a number" translates to \(4x\).
• "The square of the product of 4 and a number" translates to \((4x)^2\).
• "The sum of the number and 15" translates to \(x + 15\).

Formulate the equation

Equating the two translated parts as stated by "is":

$$(4x)^2 = x + 15$$

Answer:

• (A) \((4x)^2 = x + 15x\)
• (B) \(4x^2 = x + 15\)
• (C) \(2(4x) = x + 15\)
• (D) \((4x)^2 = x + 15\) (Correct answer)