What is (sqrt(x-3)+sqrt(x+2))^2 ?

The solution to (sqrt(x-3)+sqrt(x+2))^2 is 2x+2sqrt(x-3)sqrt(x+2)-1

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simplify (sqrt(x-3)+sqrt(x+2))^2

simplify

(x - 3 + x + 2)^{2}

2 x + 2 x - 3 x + 2 - 1

Solution steps

(x - 3 + x + 2)^{2}

Apply Perfect Square Formula:

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

(x - 3 + x + 2)^{2} = (x - 3)^{2} + 2 x - 3 x + 2 + (x + 2)^{2}

= (x - 3)^{2} + 2 x - 3 x + 2 + (x + 2)^{2}

Simplify

(x - 3)^{2} + 2 x - 3 x + 2 + (x + 2)^{2} : 2 x + 2 x - 3 x + 2 - 1

= 2 x + 2 x - 3 x + 2 - 1

\frac{6 x + 2}{( x + 1 ) ( 2 x + 1 )}

\frac{5}{( s - 2 ) ( s - 3 ) ( s - 6 )}

\frac{x}{( x ^{2} + 9 ) ^{2}}

\frac{6}{( x + 1 ) ^{4}}

(D + \frac{2}{25}) (D - \frac{1}{25})

What is (sqrt(x-3)+sqrt(x+2))^2 ?
The solution to (sqrt(x-3)+sqrt(x+2))^2 is 2x+2sqrt(x-3)sqrt(x+2)-1