What is (sqrt(5)x-1)^2 ?

The solution to (sqrt(5)x-1)^2 is 5x^2-2sqrt(5)x+1

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simplify (sqrt(5)x-1)^2

simplify

(5 x - 1)^{2}

5 x^{2} - 25 x + 1

Solution steps

(5 x - 1)^{2}

Apply Perfect Square Formula:

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

(5 x - 1)^{2} = (5 x)^{2} - 25 x \cdot 1 + 1^{2}

= (5 x)^{2} - 25 x \cdot 1 + 1^{2}

(5 x)^{2} = 5 x^{2}

- 25 x \cdot 1 = - 25 x

1^{2} = 1

= 5 x^{2} - 25 x + 1

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