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Popular >

factor x^4-2x^2+1

Solution

factor

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

Solution

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

Solution steps

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

Let

u = x^{2}

= u^{2} - 2 u + 1

Factor

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

= (u - 1)^{2}

Substitute back

u = x^{2}

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

Factor

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

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

Apply exponent rule:

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

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

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

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4 + \frac{65 - 64}{48}

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(\frac{1}{6})^{3}

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\frac{30 x ^{4} y ^{5}}{20 x ^{5} y ^{2}}

Frequently Asked Questions (FAQ)

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