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# word problems and turning them into algebraic equation to slove

This will be hard to visualize, but I'll try to explain.

Suppose that n3 sugar cubes are stacked to form an n x n x n cube. ( cube is 6 cubes wide, 6 cubes length and 6 cubes in height ) The large cube is now painted yellow. depending on where the sugar cube is positioned in the large cube, it may have one or several of it's 6 faces painted yellow.( For example, if n=1, all 6 faces are painted.)  For larger n, there are some sugar cubes with unpainted faces.

Give expressions in the variable n, n>3, for the number of sugar cubes in the n x n x n cube with 0,1,2 or 3 painted faces, respectively.  The expressions obtained , when added together, should give n3 for all n larger then equal to 3.
Why?
Use algebraic simplification to check your identity in the variable n.

### 1 Answer by Expert Tutors

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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f(0) = (n-2)^3
f(1) = 6(n-2)^2
f(2) = 12(n-2)
f(3) = 8

f(0)+f(1)+f(2)+f(3) = (n-2)^3+6(n-2)^2+12(n-2)+8 = n^3