en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (sqrt(x)+5/x)^9

Solution

expand

(x + \frac{5}{x})^{9}

Solution

x^{9} + 45 x^{3} + 900 x^{3} + 10500 + \frac{78750}{x ^{3}} + \frac{393750}{x ^{3}} + \frac{1312500 x}{x ^{5}} + \frac{2812500}{x ^{6}} + \frac{3515625}{x ^{15}} + \frac{1953125}{x ^{9}}

Solution steps

(x + \frac{5}{x})^{9}

Apply binomial theorem:

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

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

= i = 0 \sum 9 (i 9) (x)^{(9 - i)} (\frac{5}{x})^{i}

Expand summation

= \frac{9 !}{0 ! ( 9 - 0 ) !} (x)^{9} (\frac{5}{x})^{0} + \frac{9 !}{1 ! ( 9 - 1 ) !} (x)^{8} (\frac{5}{x})^{1} + \frac{9 !}{2 ! ( 9 - 2 ) !} (x)^{7} (\frac{5}{x})^{2} + \frac{9 !}{3 ! ( 9 - 3 ) !} (x)^{6} (\frac{5}{x})^{3} + \frac{9 !}{4 ! ( 9 - 4 ) !} (x)^{5} (\frac{5}{x})^{4} + \frac{9 !}{5 ! ( 9 - 5 ) !} (x)^{4} (\frac{5}{x})^{5} + \frac{9 !}{6 ! ( 9 - 6 ) !} (x)^{3} (\frac{5}{x})^{6} + \frac{9 !}{7 ! ( 9 - 7 ) !} (x)^{2} (\frac{5}{x})^{7} + \frac{9 !}{8 ! ( 9 - 8 ) !} (x)^{1} (\frac{5}{x})^{8} + \frac{9 !}{9 ! ( 9 - 9 ) !} (x)^{0} (\frac{5}{x})^{9}

Simplify

\frac{9 !}{0 ! ( 9 - 0 ) !} (x)^{9} (\frac{5}{x})^{0} : (x)^{9}

Simplify

\frac{9 !}{1 ! ( 9 - 1 ) !} (x)^{8} (\frac{5}{x})^{1} : 45 x^{3}

Simplify

\frac{9 !}{2 ! ( 9 - 2 ) !} (x)^{7} (\frac{5}{x})^{2} : \frac{900 ( x ) ^{7}}{x ^{2}}

Simplify

\frac{9 !}{3 ! ( 9 - 3 ) !} (x)^{6} (\frac{5}{x})^{3} : 10500

Simplify

\frac{9 !}{4 ! ( 9 - 4 ) !} (x)^{5} (\frac{5}{x})^{4} : \frac{78750 ( x ) ^{5}}{x ^{4}}

Simplify

\frac{9 !}{5 ! ( 9 - 5 ) !} (x)^{4} (\frac{5}{x})^{5} : \frac{393750}{x ^{3}}

Simplify

\frac{9 !}{6 ! ( 9 - 6 ) !} (x)^{3} (\frac{5}{x})^{6} : \frac{1312500 ( x ) ^{3}}{x ^{6}}

Simplify

\frac{9 !}{7 ! ( 9 - 7 ) !} (x)^{2} (\frac{5}{x})^{7} : \frac{2812500}{x ^{6}}

Simplify

\frac{9 !}{8 ! ( 9 - 8 ) !} (x)^{1} (\frac{5}{x})^{8} : \frac{3515625}{x ^{\frac{15}{2}}}

Simplify

\frac{9 !}{9 ! ( 9 - 9 ) !} (x)^{0} (\frac{5}{x})^{9} : \frac{1953125}{x ^{9}}

= (x)^{9} + 45 x^{3} + \frac{900 ( x ) ^{7}}{x ^{2}} + 10500 + \frac{78750 ( x ) ^{5}}{x ^{4}} + \frac{393750}{x ^{3}} + \frac{1312500 ( x ) ^{3}}{x ^{6}} + \frac{2812500}{x ^{6}} + \frac{3515625}{x ^{\frac{15}{2}}} + \frac{1953125}{x ^{9}}

Simplify

(x)^{9} + 45 x^{3} + \frac{900 ( x ) ^{7}}{x ^{2}} + 10500 + \frac{78750 ( x ) ^{5}}{x ^{4}} + \frac{393750}{x ^{3}} + \frac{1312500 ( x ) ^{3}}{x ^{6}} + \frac{2812500}{x ^{6}} + \frac{3515625}{x ^{\frac{15}{2}}} + \frac{1953125}{x ^{9}} : x^{\frac{9}{2}} + 45 x^{3} + 900 x^{\frac{3}{2}} + 10500 + \frac{78750}{x ^{\frac{3}{2}}} + \frac{393750}{x ^{3}} + \frac{1312500 x}{x ^{5}} + \frac{2812500}{x ^{6}} + \frac{3515625}{x ^{\frac{15}{2}}} + \frac{1953125}{x ^{9}}

= x^{\frac{9}{2}} + 45 x^{3} + 900 x^{\frac{3}{2}} + 10500 + \frac{78750}{x ^{\frac{3}{2}}} + \frac{393750}{x ^{3}} + \frac{1312500 x}{x ^{5}} + \frac{2812500}{x ^{6}} + \frac{3515625}{x ^{\frac{15}{2}}} + \frac{1953125}{x ^{9}}

Simplify

x^{\frac{9}{2}} + 45 x^{3} + 900 x^{\frac{3}{2}} + 10500 + \frac{78750}{x ^{\frac{3}{2}}} + \frac{393750}{x ^{3}} + \frac{1312500 x}{x ^{5}} + \frac{2812500}{x ^{6}} + \frac{3515625}{x ^{\frac{15}{2}}} + \frac{1953125}{x ^{9}} : x^{9} + 45 x^{3} + 900 x^{3} + 10500 + \frac{78750}{x ^{3}} + \frac{393750}{x ^{3}} + \frac{1312500 x}{x ^{5}} + \frac{2812500}{x ^{6}} + \frac{3515625}{x ^{15}} + \frac{1953125}{x ^{9}}

= x^{9} + 45 x^{3} + 900 x^{3} + 10500 + \frac{78750}{x ^{3}} + \frac{393750}{x ^{3}} + \frac{1312500 x}{x ^{5}} + \frac{2812500}{x ^{6}} + \frac{3515625}{x ^{15}} + \frac{1953125}{x ^{9}}

Popular Examples

simplify-5(sqrt(2)+sqrt(3))simplify

- 5 (2 + 3)

simplify (sqrt(x)-1/(y^2))^{12}simplify

(x - \frac{1}{y ^{2}})^{12}

expand sin(x)(2*cos(x)-1)expand

sin (x) (2 \cdot cos (x) - 1)

simplify (x+1/3)(x-2/3)simplify

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

expand (x-3)e^x expand

(x - 3) e^{x}

Frequently Asked Questions (FAQ)

What is expand (sqrt(x)+5/x)^9 ?
The solution to expand (sqrt(x)+5/x)^9 is