Final answer:
The algebraic expressions and verbal descriptions that accurately match are A, the cube of the difference of 4 times x and 9, and C, the square of the sum of 4 times x and 3 divided by the difference of x and 10. B and D do not match their descriptions.
Step-by-step explanation:
The polynomial expressions described in each row need to be matched with the correct verbal descriptions. Here are the details for each row:
- A. (4x - 9)3 accurately corresponds to "the cube of the difference of 4 times x and 9". When you cube an expression, you raise it to the power of three, which affects every term inside the parentheses, not just the variable.
- B. (3y + 10)2 does NOT correspond to "the difference of 3 times y and 10 raised to the exponent 2" because the expression is the square of the sum, not the difference.
- C. (4x + 3)2 divided by (x - 10) does correspond to "the quantity of the square of the sum of 4 times x and 3, divided by the difference of x and 10" as it matches the description of taking the square of a binomial and then dividing by another expression.
- D. (2x - 5)(7x + 7)3 corresponds to "the product of the difference of 2 times x and 5, and the cube of the sum of 7 times x and 7", not the quotient as described, making this description incorrect.
Therefore, the descriptions that accurately match the algebraic expressions are A and C.