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

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

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

factor

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

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

Solution steps

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

Simplify

4 x^{2} : (2 x)^{2}

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

Apply Difference of Two Squares Formula:

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

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

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

Apply rule:

(a) = a

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

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

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

Factor

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

Factor

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

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

46 \cdot 15

\frac{3 x - 5}{x + 1} \geq \frac{1}{3}

\frac{4 !}{2 ! ( 4 - 2 ) !}

9 n^{6} - 6561 n^{3}

10 x^{3} + 27 x^{2} + 20 x + 3 > 0

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