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

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

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

factor

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

2 (3 x^{2} + 1)

Solution steps

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

Apply Difference of Cubes Formula:

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

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

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

Refine

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

Expand

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

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

1 - v^{2} + 1 - v^{2}

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

2 x y - 5 yz - 4 x + 10 z

3 ab - 6 cc - a^{2} b + a c

3.1

What is factor (x+1)^3-(x-1)^3 ?
The solution to factor (x+1)^3-(x-1)^3 is 2(3x^2+1)