What is (xsqrt(y^2+1)+ysqrt(x^2+1))^2 ?

The solution to (xsqrt(y^2+1)+ysqrt(x^2+1))^2 is 2x^2y^2+x^2+2xysqrt(y^2+1)sqrt(x^2+1)+y^2

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simplify (xsqrt(y^2+1)+ysqrt(x^2+1))^2

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

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

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

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

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

Simplify

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

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

(- 3 x + 2 + 1) 3 x + 2

cot (x) \cdot (sec (x) + tan (x))

(4 - i)^{6}

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

\frac{4 π}{( w - π ) ^{2}}

What is (xsqrt(y^2+1)+ysqrt(x^2+1))^2 ?
The solution to (xsqrt(y^2+1)+ysqrt(x^2+1))^2 is 2x^2y^2+x^2+2xysqrt(y^2+1)sqrt(x^2+1)+y^2