Question

Use the grouping symbols to interpret the following equation: x^8 = 3(x + 4)^2. Which expression in the equation represents a product? Option 1: x^8 Option 2: 3 Option 3: (x + 4)^2 Option 4: x

Answer 1

Option 3:
`(x + 4)^2`

The expression
`\(3(x + 4)^2\)`5 represents a product because the coefficient 3 is multiplied by the square of the binomial
`\((x + 4)\)`.

Step-by-step explanation:

In the given equation,
`\(x^8 = 3(x + 4)^2\)`, the grouping symbols are represented by
`\((x + 4)^2\)`. Within these parentheses, the expression
`\(x + 4\)` is grouped together and squared.

The square operation implies multiplication, making
`\((x + 4)^2\)` equivalent to
`\((x + 4)\` times
`(x + 4)\).` Therefore, the expression
`\((x + 4)^2\)` represents a product, signifying the multiplication of
`\(x + 4\)` by itself. In contrast, the other options do not represent a product in the context of the given equation.

Option 1
`(\(x^8\))` is an eighth power of
`\(x\)`, Option 2 (3) is a constant factor, and Option 4 (x) is a single variable. Thus, the correct choice indicating the product in the equation is Option 3:
`\((x + 4)^2\)`.

This understanding is essential for correctly interpreting and manipulating the equation to solve for the variable
`\(x\)`.