A manufacturer of shipping boxes has a box shaped like a cube. The side length is (5a+4b). What is the volume of the box in terms of a and b

Question

A manufacturer of shipping boxes has a box shaped like a cube. The side length is (5a+4b). What is the volume of the box in terms of a and b?

Answer 1

The volume of any cube is

 

V = s³

 

where:

V = volume

s = side

 

Your side is given.  Therefore, the volume is

 

V = (5a + 4b)³

 

V = (5a + 4b)(5a + 4b)(5a + 4b)

 

V = (25a² + 40ab + 16b²)(5a + 4b)

 

V = 5a(25a² + 40ab + 16b²) + 4b(25a² + 40ab + 16b²)

 

V = 125a³ + 200a²b + 80ab² + 100a²b + 160ab² + 64b³

 

V = 125a³ + 300a²b + 240ab² + 64b³

Answer 2

The volume of a cube is s³, where s is the side length.  In your case, s = (5a+4b), the volume is (5a+4b)³.  You can multiply that out using the FOIL method twice:

 

(5a+4b)3

 

     = (5a+4b)(5a+4b)(5a+4b)

 

     = (25a²+40ab+16b²)(5a+4b)

 

     = 125a³ + 100a²b + 200a²b + 160ab² + 80ab² + 64b³

 

     = 125a³ + 300a²b + 240ab² + 54b³

Answer 3

Volume of cube is side lenght to the third power:

 

(5a+4b)³

 

All you need to do is expand this expression.

 

Hope this helps!