Expand and simplify (n + 2)^3 − n^3.

Expand and simplify (n + 2)³ − n³.
Write out the brackets in full:(n + 2)(n + 2)(n + 2) − n³
Use F.O.I.L. (First, Outer, Inner, Last) on first two sets of brackets:(n²+ 2n + 2n + 4)(n + 2) - n³
Simplify by combining like terms (2n + 2n = 4n):(n²+ 4n + 4)(n + 2) - n³
Multiply each term in first set of brackets by each term in second set of brackets:(n³+ 4n² + 4n + 2n² + 8n + 8) - n³
As we're not multiplying anything more, the brackets can go:n³+ 4n² + 4n + 2n² + 8n + 8 - n³
Simplify by combining like terms (n³ terms cancel, 4n² + 2n²= 6n², 4n + 8n = 12n):6n² + 12n + 8