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? Show your work.

1 Answer
xurongna_
Sep 17, 2017

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

Explanation:

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

Expand the first two brackets:
#=(25a^2 + 40ab + 16b^2)(5a+4b)#

Then, multiply the expanded bracket by the remaining bracket. (Multiply everything first by #5a#, then multiply everything by #4b#)
#=125a^3+200a^2b+80ab^2+100a^2b+160ab^2+64b^3#
#=125a^3+300a^2b+240ab^2+64b^3#

Hope this helps!

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