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

The solution to (sqrt(x+2)-3sqrt(x-2))^2 is 10x-6sqrt(x+2)sqrt(x-2)-16

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

simplify

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

10 x - 6 x + 2 x - 2 - 16

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

(x + 2)^{2} - 2 x + 2 \cdot 3 x - 2 + (3 x - 2)^{2} : 10 x - 6 x + 2 x - 2 - 16

= 10 x - 6 x + 2 x - 2 - 16

\frac{3}{2 - 3}

(8 x - 4 y + 2) + (3 x + 2 y - 5)

30 x y - 12 x + 10 y - 4

(y + 2) (y^{2} - 2 y + 4) - (y^{3} + 3)

\frac{\frac{1}{x} - \frac{1}{a}}{x - a}

What is (sqrt(x+2)-3sqrt(x-2))^2 ?
The solution to (sqrt(x+2)-3sqrt(x-2))^2 is 10x-6sqrt(x+2)sqrt(x-2)-16