Question

A manufacturer of shipping boxes has a box shaped like a cube. The side length is

Answer 1

 The volume of a cube with side length equal to x, is $V= x^{3}$, 

thus, the volume of a cube shaped box, whose side length is (5a+4b) is :

$V= (5a+4b)^{3}$,

The volume is already expressed in terms of a and b, but we can expand the expression $(5a+4b)^{3}$, as follows:

$(5a+4b)^{3} =(5a+4b)(5a+4b)^{2}= (5a+4b)[ (5a)^{2}+2(5a)(4b)+ (4b)^{2}]$

$=(5a+4b)[ 25a^{2}+40ab+ 16b^{2}]$

$=(5a)[ 25a^{2}+40ab+ 16b^{2}]+(4b)[ 25a^{2}+40ab+ 16b^{2}]$

$=125a^{3}+200a^{2} b+ 80ab^{2}+100a^{2}b+160ab^{2} + 64b^{3}$

$125a^{3}+300a^{2} b+240ab^{2} + 64b^{3}$


Answer:

$V= (5a+4b)^{3}$,

or 

$125a^{3}+300a^{2} b+240ab^{2} + 64b^{3}$