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

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

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expand sqrt(1+4x^2(x^2-1))

expand

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

2 x^{2} - 1

Solution steps

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

Expand

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

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

Factor

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

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

Apply radical rule:

assuming

a \geq 0, b \geq 0

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

Apply radical rule:

assuming

a \geq 0

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

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

Apply radical rule:

assuming

a \geq 0

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

= (2 x + 1) (2 x - 1)

Apply Difference of Two Squares Formula:

(a + b) (a - b) = a^{2} - b^{2}

a = 2 x, b = 1

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

Simplify

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

= 2 x^{2} - 1

2 - 4 (1 - 3 x = 82)

(8, - 6) x (2, - 15)

\frac{5 x - 1}{( x + 1 ) ( 1 + x + 3 x ^{2} )}

\frac{x}{( 3 x ^{2} + 2 ) ( 6 + 3 x ^{2} t + 2 t )}

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