What is (sqrt(x-1)-4)^2 ?

The solution to (sqrt(x-1)-4)^2 is x-8sqrt(x-1)+15

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simplify (sqrt(x-1)-4)^2

simplify

(x - 1 - 4)^{2}

x - 8 x - 1 + 15

Solution steps

(x - 1 - 4)^{2}

Apply Perfect Square Formula:

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

(x - 1 - 4)^{2} = (x - 1)^{2} - 2 x - 1 \cdot 4 + 4^{2}

= (x - 1)^{2} - 2 x - 1 \cdot 4 + 4^{2}

Simplify

(x - 1)^{2} - 2 x - 1 \cdot 4 + 4^{2} : x - 8 x - 1 + 15

= x - 8 x - 1 + 15

(3 x - \frac{2}{x})^{5}

- (π + 4) (π - 4) r^{2}

(2 n + 1)!

(3 - \frac{3}{2} y)^{2}

(1 + \frac{2 x}{n})^{2}