Use the grouping symbols to interpret the following equation: x8=3(x+4)2

Question

. Which expression in the equation represents a product?(1 point)
Responses

x8
Start Fraction x over 8 End Fraction

2
2

3(x+4)
3 left parenthesis x plus 4 right parenthesis

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

Answer 1

To interpret the equation \( x8 = 3(x + 4)2 \) and identify which expression represents a product, we can rewrite the equation with appropriate grouping and clarify the expressions:

1. Understand the equation: The expression on the left is represented as \( x \cdot 8 \), so it can be rewritten as \( 8x \).
2. On the right side: \( 3(x + 4)2 \) indicates the product of \( 3 \) and \( (x + 4) \) and then multiplied by \( 2 \). However, the equation can be misinterpreted without proper grouping.

Looking at the options:

• Option 1: \( x8 \) is equivalent to \( 8x \).
• Option 2: \( 2 \) is not a product expression since it is just a number.
• Option 3: \( 3(x + 4) \) is a product of \( 3 \) and \( (x + 4) \).
• Option 4: \( 3(x + 4)2 \) is a product of \( 3 \), \( (x + 4) \), and \( 2 \) together.

Final Answer: The expressions that represent a product are \( 3(x + 4) \) (Option 3) and \( 3(x + 4)2 \) (Option 4). Since the question appears to seek only one expression that represents a product, the best indication of a clear product is Option 4: \( 3(x+4)2 \), which signifies the multiplication of three distinct components together.