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Popular >

factor x^6-3x^4+3x^2-1

Solution

factor

x^{6} - 3 x^{4} + 3 x^{2} - 1

Solution

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

Solution steps

x^{6} - 3 x^{4} + 3 x^{2} - 1

Let

u = x^{2}

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

Factor

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

= (u - 1) (u - 1) (u - 1)

Substitute back

u = x^{2}

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

Factor

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

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

Factor

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

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

Factor

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

= (x + 1) (x - 1) (x + 1) (x - 1) (x + 1) (x - 1)

Refine

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

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Frequently Asked Questions (FAQ)

What is factor x^6-3x^4+3x^2-1 ?
The solution to factor x^6-3x^4+3x^2-1 is (x+1)^3(x-1)^3