What is #125x^9+64y^12# written as a sum of cubes?

1 Answer
Kavya D.
Dec 19, 2017

(#5x^3# + #4y^4#)(#25x^6# - #20x^3##y^4# + #16y^8#)

Explanation:

The skeletal equation for the sum of cubes:
#a^3# + #b^3# = (#a# + #b#)(#a^2# - #ab# + #b^2#)

In the expression #125x^9# + #64y^12#,
a = #root(3)#(#125x^9#) = #5x^3# and
b = #root(3)#(#64y^12#) = #4y^4#

Now, plug in the a and b values into the skeletal equation:

#125x^9# + #64y^12# = (#5x^3# + #4y^4#)(#25x^6# - #20x^3##y^4# + #16y^8#)

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