What is factor x^4-y^2-2x^2+1 ?

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

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factor x^4-y^2-2x^2+1

factor

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

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

Solution steps

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

Factor

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

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

Apply exponent rule:

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

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

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

Apply Difference of Two Squares Formula:

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

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

= ((x + 1) (x - 1) + y) ((x + 1) (x - 1) - y)

Simplify

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

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

100 x + 180 x + 81

\frac{- 9 p}{10}

15 a^{3} m - 20 a^{2} m

(2 b + 4)^{2}

(\frac{x ^{3}}{64}) - (\frac{64}{x ^{3}})

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