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
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#