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CAN SOMEONE JUST PLEASE ANSWER THIS ASAP FOR BRAINLIEST!!’

The volume (in cubic meters), v, of a rectangular room is given by the expression:

v = 162 - 2b^6

Where b is a positive integer and each dimension is an integer greater than 1 meter. What are three unique expressions that could represent the dimensions of the room in terms of b?

Write these three expressions as a product that equals the volume (e.g. "(expression 1)(expression 2)(expression 3)").

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kudzordzifrancis
ANSWER

The three expressions are

[tex]V = 2(9 - {b}^{3} )(9 + {b}^{3} )[/tex]

EXPLANATION

We were given the volume in cubic units to

[tex]V = 162 - 2 {b}^{6} [/tex]

If we factor 2, we get,

[tex]V = 2(81 - {b}^{6} )[/tex]

The expression in parenthesis is a difference of two squares. But you may not recognize it at first sight.

[tex]V = 2( {9}^{2} - ({b}^{3})^{2} )[/tex]

This further gives us.

[tex]V = (2)(9 - {b}^{3} )(9 + {b}^{3} )[/tex]

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