What is (sqrt(a^2+b^2)+sqrt(c^2+d^2))^2 ?

The solution to (sqrt(a^2+b^2)+sqrt(c^2+d^2))^2 is a^2+b^2+2sqrt(a^2+b^2)sqrt(c^2+d^2)+c^2+d^2

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simplify (sqrt(a^2+b^2)+sqrt(c^2+d^2))^2

simplify

(a^{2} + b^{2} + c^{2} + d^{2})^{2}

a^{2} + b^{2} + 2 a^{2} + b^{2} c^{2} + d^{2} + c^{2} + d^{2}

Solution steps

(a^{2} + b^{2} + c^{2} + d^{2})^{2}

Apply Perfect Square Formula:

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

(a^{2} + b^{2} + c^{2} + d^{2})^{2} = (a^{2} + b^{2})^{2} + 2 a^{2} + b^{2} c^{2} + d^{2} + (c^{2} + d^{2})^{2}

= (a^{2} + b^{2})^{2} + 2 a^{2} + b^{2} c^{2} + d^{2} + (c^{2} + d^{2})^{2}

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

(c^{2} + d^{2})^{2} = c^{2} + d^{2}

= a^{2} + b^{2} + 2 a^{2} + b^{2} c^{2} + d^{2} + c^{2} + d^{2}

4 (a + e)

5 (6 + 7)

(z - 1 + i)^{2}

\frac{( 2 x - 1 ) ( x + 3 )}{x ^{3} - 8}

(r - 1)^{3} (r + 4 - 2 i)^{4} r

What is (sqrt(a^2+b^2)+sqrt(c^2+d^2))^2 ?
The solution to (sqrt(a^2+b^2)+sqrt(c^2+d^2))^2 is a^2+b^2+2sqrt(a^2+b^2)sqrt(c^2+d^2)+c^2+d^2