Simplification

To solve the given expression, observe that the structure of the numerator and the denominator follows the form of a difference and a sum of cubes, respectively. The expression is:

We can rewrite this in terms of cube formulas. Let and . Then the expression becomes:

Recall the algebraic identity for the difference of cubes:

Notice that the denominator exactly matches the second factor of the identity:

Thus, the entire fraction simplifies by canceling the common terms in the numerator and the denominator:

Now substitute back the values of and :

Therefore, the value that should replace the question mark is:

578

To determine who among P, Q, R, S, T is the heaviest, we analyze the given conditions:

1. R is heavier than only P. This implies R is the second lightest.
2. S is lighter than Q and heavier than T. This means S is heavier than T and lighter than Q.

From these conditions, we deduce the order of weights:

1. P is the lightest.
2. R is heavier than P.
3. T is heavier than R but lighter than S.
4. S is heavier than T but lighter than Q.
5. Q is the heaviest.

Thus, based on the logical deductions, the heaviest person among them is Q.

To find the value of 28 mod 3, we need to determine the remainder when 28 is divided by 3.

First, perform the division:

which equals 9 with a remainder of 1, because:

The remainder r when dividing 28 by 3 is 1. Therefore:

So, the value of 28 mod 3 is 1.