For a regular cube:
side length = \(s[tex]
volume = [tex]s^3\)
This problem has a lot of distributing. I suggest you use a grid to make sure each term is distributed (see attached image on how to do this)
For our problem:
side length = \(s=5a+4b\)
\(s^2=25a^2+40ab+16b^2\) (use FOIL)
\(s^3=s^2\times\s=(25a^2+40ab+16b^2)(5a+4b)\)
Multiplying 5a(25a²+40ab+16b²) = \(125a^3+200a^2b+80ab^2\)
Multiplying 4b(25a²+40ab+16b²) = \(100a^2b+160ab^2+64b^3\)
Combine like terms. (200a²b + 100a²b = 300a²b, 80ab² + 160ab² = 240ab²)
volume = s³ = \(\boxed{125a^3+300a^2b+240ab^2+64b^3}\)
