The volume of a cube with side length equal to x, is [tex]V= x^{3} [/tex],
thus, the volume of a cube shaped box, whose side length is (5a+4b) is :
[tex]V= (5a+4b)^{3} [/tex],
The volume is already expressed in terms of a and b, but we can expand the expression [tex](5a+4b)^{3} [/tex], as follows:
[tex](5a+4b)^{3} =(5a+4b)(5a+4b)^{2}= (5a+4b)[ (5a)^{2}+2(5a)(4b)+ (4b)^{2}][/tex]
[tex]=(5a+4b)[ 25a^{2}+40ab+ 16b^{2}][/tex]
[tex]=(5a)[ 25a^{2}+40ab+ 16b^{2}]+(4b)[ 25a^{2}+40ab+ 16b^{2}][/tex]
[tex]=125a^{3}+200a^{2} b+ 80ab^{2}+100a^{2}b+160ab^{2} + 64b^{3}[/tex]
[tex]125a^{3}+300a^{2} b+240ab^{2} + 64b^{3}[/tex]
Answer:
[tex]V= (5a+4b)^{3} [/tex],
or
[tex]125a^{3}+300a^{2} b+240ab^{2} + 64b^{3}[/tex]
