What is (sqrt(x+1)+sqrt(12-x))^2 ?

The solution to (sqrt(x+1)+sqrt(12-x))^2 is 2sqrt(x+1)sqrt(12-x)+13

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simplify (sqrt(x+1)+sqrt(12-x))^2

simplify

(x + 1 + 12 - x)^{2}

2 x + 1 12 - x + 13

Solution steps

(x + 1 + 12 - x)^{2}

Apply Perfect Square Formula:

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

(x + 1 + 12 - x)^{2} = (x + 1)^{2} + 2 x + 1 12 - x + (12 - x)^{2}

= (x + 1)^{2} + 2 x + 1 12 - x + (12 - x)^{2}

Simplify

(x + 1)^{2} + 2 x + 1 12 - x + (12 - x)^{2} : 2 x + 1 12 - x + 13

= 2 x + 1 12 - x + 13

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What is (sqrt(x+1)+sqrt(12-x))^2 ?
The solution to (sqrt(x+1)+sqrt(12-x))^2 is 2sqrt(x+1)sqrt(12-x)+13