we know that
The volume of the first cube is
(5h^2)^3
while
the volume of the second cube is
(3k)^3
so
their total volume is
(5h^2)^3 + (3k)^3
We can use the special formula for factoring a sum of two cubes:
x^3 + y^3 = (x + y)(x^2 - xy + y^2)
(5h^2)^3 + (3k)^3 = (5h^2 + 3k)((5h^2)^2 - (5h^2)(3k) + (3k)^2)
= (5h^2 + 3k)(25h^4 - 15(h^2)(k) + 9k^2)
the answer is
[tex](5 h^{2} +3k)(25 h^{4}-15 h^{2}k+9k^{2} )[/tex]
