Question

Which description is paired with its correct expression?

Option 1: O seven less than the quotient of two and a number squared, increased by six; (2/n^2 - 7)
Option 2: O nine times the difference of a number cubed and three; (9(n^3 - 3))
Option 3: O eight more than the quotient of a number squared and four, decreased by seven; ((n^2 / 4 + 8) - 7)
Option 4: O twice the difference of a number cubed and eight; (2(n^3 - 8))

Answer 1

The correct match between the description and the expression is Option 2, which is 'nine times the difference of a number cubed and three'; (9(n^3 - 3)). The other options do not accurately pair the descriptions with their mathematical expressions.

Step-by-step explanation:

The correct pairing of the description with its expression is Option 2: nine times the difference of a number cubed and three; (9(n^3 - 3)). In this case, the algebraic expression accurately reflects the described mathematical operation.

Let's review why the other options are incorrect:

• Option 1 suggests seven less than the quotient of two and a number squared, increased by six. The correct form should include seven being subtracted after the increase by six to reflect 'increased by six, then seven less,' which would be (2/n^2 + 6 - 7) or simplified as (2/n^2 - 1).
• Option 3 describes eight more than the quotient of a number squared and four, decreased by seven. The correct form would first add eight to the quotient of a number squared and four, then subtract seven, making the correct expression ((n^2 / 4) + 1), not the given ((n^2 / 4 + 8) - 7).
• Option 4 is accurate as written and doesn't require any rectification: twice the difference of a number cubed and eight; (2(n^3 - 8)).

This explanation helps in understanding that expressions must match their descriptions in terms of order and grouping of terms.