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

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

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

simplify

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

2 x^{3} + 6 x

Solution steps

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

Expand

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

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

Expand

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

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

Group like terms

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

Add similar elements:

x^{3} + x^{3} = 2 x^{3}

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

Add similar elements:

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

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

Add similar elements:

3 x + 3 x = 6 x

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

Subtract the numbers:

1 - 1 = 0

= 2 x^{3} + 6 x

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