Write an algebraic expression to represent the verbal expression

the difference between the product of 4 and a number and the square of the number

You set it up like this.

It says "the difference", so you put a minus sign: -

It says that the minuend, or the part being taken away from is a quantity equal to the product of 4 and "some number" (we'll use x), so now you have: (4 * x) -

Next, it says the subtrahend, or part being removed, is the square of "the number", meaning we use the "some number", x, from before, so now you have: (4 * x) - x^2