the quotient of the product of 32 and 15 and the difference of 17 and 9 as a numerical expression?

The term "quotient" refers to the result of division. The term "product" refers to the result of multiplication. The term "difference" refers to the result of subtraction.

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Here, we want the quotient of a product and a difference. This means the product will be divided by the difference. The product is the product of 32 and 15, so its value is (32×15). The difference is the difference of 17 and 9, so its value is (17 -9).

Then the desired numerical expression is ...

[tex]\boxed{\dfrac{32\times15}{17-9}}[/tex]

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Additional comment

The result of evaluating this expression is ...

(32×15)/(17 -9) = 480/8 = 60

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For quotients and differences, the order of the operands matters. Our convention is that "the quotient of A and B" means "A/B", and "the difference of A and B" means "A-B".

In general English usage (not specific to a formal math problem), the term "difference" often is used to mean "the positive difference." That is, the wording "the difference between 3 and 4" would generally refer to the value 1 (not -1).