What is expand (x^{1/4}-1)^4 ?

The solution to expand (x^{1/4}-1)^4 is x-4x^{3/4}+6x^{1/2}-4x^{1/4}+1

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expand (x^{1/4}-1)^4

expand

(x^{\frac{1}{4}} - 1)^{4}

x - 4 x^{\frac{3}{4}} + 6 x^{\frac{1}{2}} - 4 x^{\frac{1}{4}} + 1

Solution steps

(x^{\frac{1}{4}} - 1)^{4}

Apply binomial theorem:

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

a = x^{\frac{1}{4}}, b = - 1

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

= x - 4 x^{\frac{3}{4}} + 6 x^{\frac{1}{2}} - 4 x^{\frac{1}{4}} + 1

4 e^{2 e^{2} + 2} + \frac{1}{( e + 1 ) ^{2}} + 9 e^{4}

2 (15 + 26)

\frac{d}{d y} ((x) (x^{2} + y^{2} - 4 x + 10 y - 12))

\frac{3}{( x + 2 ) ( 2 x + 1 )}

10 (\frac{2}{5} - 2 y)

What is expand (x^{1/4}-1)^4 ?
The solution to expand (x^{1/4}-1)^4 is x-4x^{3/4}+6x^{1/2}-4x^{1/4}+1