What is factor cos^8(x)-2cos^4(x)+1 ?

The solution to factor cos^8(x)-2cos^4(x)+1 is (cos^2(x)+1)^2(cos(x)+1)^2(cos(x)-1)^2

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factor cos^8(x)-2cos^4(x)+1

factor

cos^{8} (x) - 2 cos^{4} (x) + 1

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

Solution steps

cos^{8} (x) - 2 cos^{4} (x) + 1

Let

u = cos^{2} (x)

= 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 = cos^{2} (x)

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

Factor

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

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

Factor

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

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

Refine

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

(sin (8 x))^{4}

x - (x - y)

4 9^{2} - 16

25 e^{4} - 30 e^{2} f + 9 f^{2}

[- 22.22]

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