Question

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)").

Answer 1

7(b^2 -2)(b^2 +2)

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.