What is factor x^8-8x^4+16 ?

The solution to factor x^8-8x^4+16 is (x^2+2)^2(x+sqrt(2))^2(x-sqrt(2))^2

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factor x^8-8x^4+16

factor

x^{8} - 8 x^{4} + 16

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

Solution steps

x^{8} - 8 x^{4} + 16

Let

u = x^{2}

= u^{4} - 8 u^{2} + 16

Factor

u^{4} - 8 u^{2} + 16 : (u + 2) (u - 2) (u + 2) (u - 2)

= (u + 2) (u - 2) (u + 2) (u - 2)

Substitute back

u = x^{2}

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

Refine

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

Apply exponent rule:

a^{m} b^{m} = (ab)^{m},

assuming

a \geq 0, b \geq 0

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

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

Factor

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

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

2^{- x}

\frac{1}{2 \cdot 0.0 5 ^{2}} lo g_{e} (\frac{2}{0.01})

lo g_{c} (x^{2} y^{4} z)

∣ 3 x - 5 ∣ - 11 = - 9

7 + 2 x^{2} = 11

What is factor x^8-8x^4+16 ?
The solution to factor x^8-8x^4+16 is (x^2+2)^2(x+sqrt(2))^2(x-sqrt(2))^2