What is (sqrt(x+9)-sqrt(x))^2 ?

The solution to (sqrt(x+9)-sqrt(x))^2 is 2x-2sqrt(x)sqrt(x+9)+9

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simplify (sqrt(x+9)-sqrt(x))^2

simplify

(x + 9 - x)^{2}

2 x - 2 x x + 9 + 9

Solution steps

(x + 9 - x)^{2}

Apply Perfect Square Formula:

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

(x + 9 - x)^{2} = (x + 9)^{2} - 2 x + 9 x + (x)^{2}

= (x + 9)^{2} - 2 x + 9 x + (x)^{2}

Simplify

(x + 9)^{2} - 2 x + 9 x + (x)^{2} : 2 x - 2 x x + 9 + 9

= 2 x - 2 x x + 9 + 9

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What is (sqrt(x+9)-sqrt(x))^2 ?
The solution to (sqrt(x+9)-sqrt(x))^2 is 2x-2sqrt(x)sqrt(x+9)+9