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
Jim G.
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#

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