What is (sqrt(x+15)+sqrt(x))^2 ?

The solution to (sqrt(x+15)+sqrt(x))^2 is 2x+2sqrt(x)sqrt(x+15)+15

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simplify (sqrt(x+15)+sqrt(x))^2

simplify

(x + 15 + x)^{2}

2 x + 2 x x + 15 + 15

Solution steps

(x + 15 + x)^{2}

Apply Perfect Square Formula:

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

(x + 15 + x)^{2} = (x + 15)^{2} + 2 x + 15 x + (x)^{2}

= (x + 15)^{2} + 2 x + 15 x + (x)^{2}

Simplify

(x + 15)^{2} + 2 x + 15 x + (x)^{2} : 2 x + 2 x x + 15 + 15

= 2 x + 2 x x + 15 + 15

2 (2 x cos^{3} (x) - 3 x^{2} cos^{2} (x) sin (x))

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

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

1 + \frac{sin ^{2} ( w x )}{cos ^{2} ( w x )}

(x - 1)^{4}

What is (sqrt(x+15)+sqrt(x))^2 ?
The solution to (sqrt(x+15)+sqrt(x))^2 is 2x+2sqrt(x)sqrt(x+15)+15