What is expand (1+2/5 x)^5 ?

The solution to expand (1+2/5 x)^5 is 1+2x+(8x^2)/5+(16x^3)/(25)+(16x^4)/(125)+(32x^5)/(3125)

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expand (1+2/5 x)^5

expand

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

1 + 2 x + \frac{8 x ^{2}}{5} + \frac{16 x ^{3}}{25} + \frac{16 x ^{4}}{125} + \frac{32 x ^{5}}{3125}

Solution steps

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

Apply binomial theorem:

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

a = 1, b = \frac{2}{5} x

= i = 0 \sum 5 (i 5) \cdot 1^{(5 - i)} (\frac{2}{5} x)^{i}

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} \cdot 1^{5} (\frac{2}{5} x)^{0} : 1

Simplify

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

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} \cdot 1^{3} (\frac{2}{5} x)^{2} : \frac{8 x ^{2}}{5}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} \cdot 1^{2} (\frac{2}{5} x)^{3} : \frac{16 x ^{3}}{25}

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} \cdot 1^{1} (\frac{2}{5} x)^{4} : \frac{16 x ^{4}}{125}

Simplify

\frac{5 !}{5 ! ( 5 - 5 ) !} \cdot 1^{0} (\frac{2}{5} x)^{5} : \frac{32 x ^{5}}{3125}

= 1 + 2 x + \frac{8 x ^{2}}{5} + \frac{16 x ^{3}}{25} + \frac{16 x ^{4}}{125} + \frac{32 x ^{5}}{3125}

\frac{( 36 x + 1 ) ^{\frac{3}{2}} - 1}{54}

\frac{( x + 1 ) ( x - 6 )}{2 ( x + 2 ) ( x - 3 )}

cos (x) (x + y)

(\frac{3 x ^{2}}{2} - \frac{1}{3 x})^{15}

5 (1 - e^{- \frac{t}{2}})

What is expand (1+2/5 x)^5 ?
The solution to expand (1+2/5 x)^5 is 1+2x+(8x^2)/5+(16x^3)/(25)+(16x^4)/(125)+(32x^5)/(3125)