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

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

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

simplify

(x - 1)^{2} - (x - 2)^{2}

2 x - 3

Solution steps

(x - 1)^{2} - (x - 2)^{2}

(x - 1)^{2} = x - 2 x + 1

(x - 2)^{2} = x - 4 x + 4

= x - 2 x + 1 - (x - 4 x + 4)

Expand

- (x - 4 x + 4) : - x + 4 x - 4

= x - 2 x + 1 - x + 4 x - 4

Group like terms

= x - x - 2 x + 4 x + 1 - 4

Add similar elements:

x - x = 0

= - 2 x + 4 x + 1 - 4

Add similar elements:

- 2 x + 4 x = 2 x

= 2 x + 1 - 4

Subtract the numbers:

1 - 4 = - 3

= 2 x - 3

10 x^{4} - x^{2} - 3

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

3 a^{8} - 192 a^{2}

(2 u^{5} - 13 u^{4}) + (8 u^{4} + u^{5})

- 2 (a - 3 b + c)

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