What is expand (x^{2/3}-2x^{1/3})^4 ?

The solution to expand (x^{2/3}-2x^{1/3})^4 is x^{8/3}-8x^{7/3}+24x^2-32x^{5/3}+16x^{4/3}

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expand (x^{2/3}-2x^{1/3})^4

expand

(x^{\frac{2}{3}} - 2 x^{\frac{1}{3}})^{4}

x^{\frac{8}{3}} - 8 x^{\frac{7}{3}} + 24 x^{2} - 32 x^{\frac{5}{3}} + 16 x^{\frac{4}{3}}

Solution steps

(x^{\frac{2}{3}} - 2 x^{\frac{1}{3}})^{4}

Apply binomial theorem:

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

a = x^{\frac{2}{3}}, b = - 2 x^{\frac{1}{3}}

= i = 0 \sum 4 (i 4) (x^{\frac{2}{3}})^{(4 - i)} (- 2 x^{\frac{1}{3}})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (x^{\frac{2}{3}})^{4} (- 2 x^{\frac{1}{3}})^{0} : x^{\frac{8}{3}}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{\frac{2}{3}})^{3} (- 2 x^{\frac{1}{3}})^{1} : - 8 x^{\frac{7}{3}}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (x^{\frac{2}{3}})^{2} (- 2 x^{\frac{1}{3}})^{2} : 24 x^{2}

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (x^{\frac{2}{3}})^{1} (- 2 x^{\frac{1}{3}})^{3} : - 32 x^{\frac{5}{3}}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (x^{\frac{2}{3}})^{0} (- 2 x^{\frac{1}{3}})^{4} : 16 x^{\frac{4}{3}}

= x^{\frac{8}{3}} - 8 x^{\frac{7}{3}} + 24 x^{2} - 32 x^{\frac{5}{3}} + 16 x^{\frac{4}{3}}

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

R A TE (5, 94.25, - 270.34 - 40)

\frac{( a + 2 ) + ( a + 3 ) !}{( a + 2 ) ! ( a + 4 )}

What is expand (x^{2/3}-2x^{1/3})^4 ?
The solution to expand (x^{2/3}-2x^{1/3})^4 is x^{8/3}-8x^{7/3}+24x^2-32x^{5/3}+16x^{4/3}