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) ").

Question

Mathematics

Jensen King

20 November, 01:11

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) ").

+5

Answers (1)

Know the Answer?

Georgia Ochoa · Answer 1

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.