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

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

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simplify (sqrt(x^2+1)+sqrt(x^2-1))^2

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

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

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

\frac{27 x ^{4}}{( 15 - x ) ^{2}}

(2 x + x^{3})^{2}

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

5 x (x + \frac{3}{4}) (x - \frac{1}{2})

(a x - b y) (c x + d y)

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