The volume (in cubic meters), v, of a rectangular room is given by the expression:
v = 7b^4-28
where b is a positive integer and each dimension is a positive integer too. what are three unique expressions that could represent the dimensions of the room?
write these three expressions as a product that equals the volume (e.g. "(expression 1)(expression 2)(expression 3)").

  7(b^2 -2)(b^2 +2)

Step-by-step explanation:

Factoring the common factor 7 from both terms, you get the difference of squares. That can also be factored.

  v = 7(b^4 -4) = 7(b^2 -2)(b^2 +2)

The difference b^2-2 will have irrational factors, so does not meet the problem requirements. This is the factorization over integers.

The events are independent. They are not related at all. This is because you put the card back in, keeping the total number of cards the same. If you did not put the card back, then the second draw (selecting the queen) would be dependent on the first event (selecting the king)

The probability of picking a king is 4/52 = 1/13

If you do not put the card back, then there are 52-1 = 51 cards left and 4 queens, so 4/51 is the probability of getting a queen. Again, this is assuming you do not put the first card back. Putting that first card back would make the queen's probability 4/52 = 1/13, which is the same as selecting that king.