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
