Question

Use the grouping symbols to interpret the following equation: x8=3(x+4)2. Which expression in the equation represents a product?(1 point)
Responses

2
2

x8
Start Fraction x over 8 End Fraction

3(x+4)2
Start Fraction 3 left parenthesis x plus 4 right parenthesis over 2 End Fraction

3(x+4)

Answer 1

To interpret the equation \( x8 = 3(x + 4)2 \), we first need to recognize the grouping symbols and the components of the equation.

The original equation appears to use non-standard formatting, but we can rewrite it with appropriate symbols for clarity. Assuming \( x8 \) represents \( x \times 8 \) and \( (x+4)2 \) represents \( (x+4) \times 2 \), the equation reads:

\[ 8x = 3(x + 4) \times 2 \]

Now, let's analyze the options given for the expression that represents a product:

1. **2**: This is just a numeric value, not a product.
2. **\( x8 \)** or \( 8x \): This represents a multiplication (i.e., \( 8 \times x \)), so it is a product.
3. **\( 3(x + 4)2 \)** or \( 3(x + 4) \times 2 \): This is also a product because it is multiplying \( 3 \) with \( (x + 4) \) and \( 2 \).
4. **\( 3(x + 4) \)**: While this expression itself doesn't include \( 2 \), it does represent a product of \( 3 \) and \( (x + 4) \).

Based on the interpretations, both **\( 8x \)** and **\( 3(x + 4) \times 2 \)** represent products. However, since only one answer is to be chosen, and the question specifically refers to expressions within the equation without the numeric constant, the best answer considering complete product expression representation is:

**\( 3(x + 4)2 \)** represents a product.

However, if we must pick only one option and consider products strictly among the presented answers, then **\( 3(x + 4) \)** is also considered a product.

If you prefer clarity or specificity from the list, you may choose **\( 3(x + 4)2 \)**, as it directly includes the multiplication with 2.