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

The solution to expand (sqrt(x)-1)^4 is x^2-4xsqrt(x)+6x-4sqrt(x)+1

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expand (sqrt(x)-1)^4

expand

(x - 1)^{4}

x^{2} - 4 x x + 6 x - 4 x + 1

Solution steps

(x - 1)^{4}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = x, b = - 1

= i = 0 \sum 4 (i 4) (x)^{(4 - i)} (- 1)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} (- 1)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} (- 1)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} (- 1)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} (- 1)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} (- 1)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x)^{4} (- 1)^{0} : x^{2}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x)^{3} (- 1)^{1} : - 4 (x)^{3}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x)^{2} (- 1)^{2} : 6 x

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x)^{1} (- 1)^{3} : - 4 x

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x)^{0} (- 1)^{4} : 1

= x^{2} - 4 (x)^{3} + 6 x - 4 x + 1

Simplify

(x)^{3} : x x

= x^{2} - 4 x x + 6 x - 4 x + 1

- \frac{2 x ( - x ^{2} + 12 )}{( x ^{2} + 4 ) ^{3}}

- \frac{5 x - 7}{( x - 3 ) ^{3}}

\frac{z}{( z ^{2} + 2 z + 2 ) ^{2}}

\frac{18 x ^{2} + 3 x + 6}{( 3 x + 1 ) ^{3}}

(4 + 4 sin (θ))^{2}

What is expand (sqrt(x)-1)^4 ?
The solution to expand (sqrt(x)-1)^4 is x^2-4xsqrt(x)+6x-4sqrt(x)+1