Question

The product of x and the sum of 6 and 8 times the square of x

Answer 1

"·" - product

"+" - sum

x² - square of x

Answer: x · (6 + 8 · x²) = x(6 + 8x²)

Answer 2

The expression "the product of x and the sum of 6 and 8 times the square of x" can be written as
`\( x \cdot (6 + 8x^2) \)`.

The mathematical expression "the product of x and the sum of 6 and 8 times the square of x" is represented as
`\( x \cdot (6 + 8x^2) \)`. To simplify, distribute x into the parentheses, yielding 6x + 8x^3. This expression captures the specified operation, where x is multiplied by the sum of 6 and 8 times the square of x.

It is essential to follow the order of operations, ensuring that the square of x is calculated first, then multiplied by 8, and finally added to 6 before multiplying the result by x. This expression forms the algebraic representation of the described mathematical operation.