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?

1 Answer
Sep 19, 2017

"volume "=125a^3+64b^3+300a^2b+240ab^2

Explanation:

"given a cube of side n then volume (V) is"

•color(white)(x)V=n^3

"here the side "=(5a+4b)

rArrV=(5a+4b)^3

color(red)(bar(ul(|color(white)(2/2)color(black)((a+b)^3=a^3+b^3+3ab(a+b))color(white)(2/2)|)))

"here "a=5a" and "b=4b

rArr(5a+4b)^3

=(5a)^3+(4b)^3+3(5a)(4b)(5a+4b)

=125a^3+64b^3+60ab(5a+4b)

=125a^3+64b^3+300a^2b+240ab^2