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

The solution to (sqrt(x-2)-3)^2 is x-6sqrt(x-2)+7

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

simplify

(x - 2 - 3)^{2}

x - 6 x - 2 + 7

Solution steps

(x - 2 - 3)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

(x - 2)^{2} - 2 x - 2 \cdot 3 + 3^{2} : x - 6 x - 2 + 7

= x - 6 x - 2 + 7

\frac{x - 1}{( x - 3 ) ( x + 1 )}

- a (2 a x + b) sin (a x^{2} + b x + c)

(3 - 4 x - 3) (3 + 4 x - 3)

x d y - (y + x y^{3} (1 + ln (x)) d x = 0)

\frac{d}{d x} ((c) (1 - \frac{b}{c}))