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

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

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factor 16-8x^4+x^8

factor

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

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

Solution steps

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

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}

\frac{x ^{3} - y ^{3}}{x - y}

\frac{d ^{4}}{d x ^{4}} ((y) (e^{x}))

x^{\frac{3}{2}} - 8

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

10 0^{2} 1

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