What is (n+1)^3+(n-1)^3 ?

The solution to (n+1)^3+(n-1)^3 is 2n^3+6n

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simplify (n+1)^3+(n-1)^3

simplify

(n + 1)^{3} + (n - 1)^{3}

2 n^{3} + 6 n

Solution steps

(n + 1)^{3} + (n - 1)^{3}

Expand

(n + 1)^{3} : n^{3} + 3 n^{2} + 3 n + 1

= n^{3} + 3 n^{2} + 3 n + 1 + (n - 1)^{3}

Expand

(n - 1)^{3} : n^{3} - 3 n^{2} + 3 n - 1

= n^{3} + 3 n^{2} + 3 n + 1 + n^{3} - 3 n^{2} + 3 n - 1

Group like terms

= n^{3} + n^{3} + 3 n^{2} - 3 n^{2} + 3 n + 3 n + 1 - 1

Add similar elements:

n^{3} + n^{3} = 2 n^{3}

= 2 n^{3} + 3 n^{2} - 3 n^{2} + 3 n + 3 n + 1 - 1

Add similar elements:

3 n^{2} - 3 n^{2} = 0

= 2 n^{3} + 3 n + 3 n + 1 - 1

Add similar elements:

3 n + 3 n = 6 n

= 2 n^{3} + 6 n + 1 - 1

Subtract the numbers:

1 - 1 = 0

= 2 n^{3} + 6 n

20 lo g_{10} (100)

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125 b