What is expand (x+2/3)^5 ?

The solution to expand (x+2/3)^5 is x^5+(10x^4)/3+(40x^3)/9+(80x^2)/(27)+(80x)/(81)+32/243

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expand (x+2/3)^5

expand

(x + \frac{2}{3})^{5}

x^{5} + \frac{10 x ^{4}}{3} + \frac{40 x ^{3}}{9} + \frac{80 x ^{2}}{27} + \frac{80 x}{81} + \frac{32}{243}

Solution steps

(x + \frac{2}{3})^{5}

Apply binomial theorem:

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

a = x, b = \frac{2}{3}

= i = 0 \sum 5 (i 5) x^{(5 - i)} (\frac{2}{3})^{i}

Expand summation

= \frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} (\frac{2}{3})^{0} + \frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} (\frac{2}{3})^{1} + \frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (\frac{2}{3})^{2} + \frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (\frac{2}{3})^{3} + \frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (\frac{2}{3})^{4} + \frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} (\frac{2}{3})^{5}

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} x^{5} (\frac{2}{3})^{0} : x^{5}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} x^{4} (\frac{2}{3})^{1} : \frac{10 x ^{4}}{3}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} x^{3} (\frac{2}{3})^{2} : \frac{40 x ^{3}}{9}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} x^{2} (\frac{2}{3})^{3} : \frac{80 x ^{2}}{27}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} x^{1} (\frac{2}{3})^{4} : \frac{80 x}{81}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} x^{0} (\frac{2}{3})^{5} : \frac{32}{243}

= x^{5} + \frac{10 x ^{4}}{3} + \frac{40 x ^{3}}{9} + \frac{80 x ^{2}}{27} + \frac{80 x}{81} + \frac{32}{243}

(y^{2} - 2 x y) d x + x^{2} d y

(1 + cos^{2} (x)) (cos (x))

(x^{4} + 2 y) d x - x d y

- \frac{1}{3} P (- 2, - 3)

e^{x} (5 - x)

What is expand (x+2/3)^5 ?
The solution to expand (x+2/3)^5 is x^5+(10x^4)/3+(40x^3)/9+(80x^2)/(27)+(80x)/(81)+32/243