What is expand (y^{7/4}-1)^4 ?

The solution to expand (y^{7/4}-1)^4 is y^7-4y^{21/4}+6y^{7/2}-4y^{7/4}+1

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expand (y^{7/4}-1)^4

expand

(y^{\frac{7}{4}} - 1)^{4}

y^{7} - 4 y^{\frac{21}{4}} + 6 y^{\frac{7}{2}} - 4 y^{\frac{7}{4}} + 1

Solution steps

(y^{\frac{7}{4}} - 1)^{4}

Apply binomial theorem:

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

a = y^{\frac{7}{4}}, b = - 1

= i = 0 \sum 4 (i 4) (y^{\frac{7}{4}})^{(4 - i)} (- 1)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} (y^{\frac{7}{4}})^{4} (- 1)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} (y^{\frac{7}{4}})^{3} (- 1)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} (y^{\frac{7}{4}})^{2} (- 1)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} (y^{\frac{7}{4}})^{1} (- 1)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} (y^{\frac{7}{4}})^{0} (- 1)^{4}

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (y^{\frac{7}{4}})^{4} (- 1)^{0} : y^{7}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (y^{\frac{7}{4}})^{3} (- 1)^{1} : - 4 y^{\frac{21}{4}}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (y^{\frac{7}{4}})^{2} (- 1)^{2} : 6 y^{\frac{7}{2}}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (y^{\frac{7}{4}})^{1} (- 1)^{3} : - 4 y^{\frac{7}{4}}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (y^{\frac{7}{4}})^{0} (- 1)^{4} : 1

= y^{7} - 4 y^{\frac{21}{4}} + 6 y^{\frac{7}{2}} - 4 y^{\frac{7}{4}} + 1

i (x + y i)^{4}

sin (2 t) \cdot x (t - π)

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

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

x (x - \frac{1}{2})

What is expand (y^{7/4}-1)^4 ?
The solution to expand (y^{7/4}-1)^4 is y^7-4y^{21/4}+6y^{7/2}-4y^{7/4}+1