What is factor (x^2-1)^3-27 ?

The solution to factor (x^2-1)^3-27 is (x+2)(x-2)(x^4+x^2+7)

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factor (x^2-1)^3-27

factor

(x^{2} - 1)^{3} - 27

(x + 2) (x - 2) (x^{4} + x^{2} + 7)

Solution steps

(x^{2} - 1)^{3} - 27

Rewrite

27

3^{3}

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

Apply Difference of Cubes Formula:

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

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

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

Refine

= (x^{2} - 4) ((x^{2} - 1)^{2} + 3 (x^{2} - 1) + 9)

Factor

x^{2} - 4 : (x + 2) (x - 2)

= (x + 2) (x - 2) ((x^{2} - 1)^{2} + 3 (x^{2} - 1) + 9)

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

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

= (x + 2) (x - 2) ((x + 1)^{2} (x - 1)^{2} + 3 (x + 1) (x - 1) + 9)

Expand

(x + 1)^{2} (x - 1)^{2} + 3 (x + 1) (x - 1) + 9 : x^{4} + x^{2} + 7

= (x + 2) (x - 2) (x^{4} + x^{2} + 7)

(x + y) - a^{2}

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

x^{3} + 0 x^{2} - 52 x + 90

d e^{8 t + 6}

(x^{2} - 3 x) - 36

What is factor (x^2-1)^3-27 ?
The solution to factor (x^2-1)^3-27 is (x+2)(x-2)(x^4+x^2+7)