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

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

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expand (x^{1/4}+y^{1/4})^4

expand

(x^{\frac{1}{4}} + y^{\frac{1}{4}})^{4}

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

Solution steps

(x^{\frac{1}{4}} + y^{\frac{1}{4}})^{4}

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

2 l e f t (a^{2} + 3 a - 4)

\frac{1}{s ^{n} ( s - 3 )}

- 27 x^{\frac{1}{3}} (2 x^{2} + 14 x + 42)

sin (\frac{π}{6})

(u^{\frac{3}{2}} + 3 u)^{2}

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