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Popular >

factor z^8-2z^4+1

Solution

factor

z^{8} - 2 z^{4} + 1

Solution

(z^{2} + 1)^{2} (z + 1)^{2} (z - 1)^{2}

Solution steps

z^{8} - 2 z^{4} + 1

Let

u = z^{2}

= u^{4} - 2 u^{2} + 1

Factor

u^{4} - 2 u^{2} + 1 : (u + 1) (u - 1) (u + 1) (u - 1)

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

Substitute back

u = z^{2}

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

Factor

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

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

Factor

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

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

Refine

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

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Frequently Asked Questions (FAQ)

What is factor z^8-2z^4+1 ?
The solution to factor z^8-2z^4+1 is (z^2+1)^2(z+1)^2(z-1)^2