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

The solution to expand (3x^2-2/x)^5 is 243x^{10}-810x^7+1080x^4-720x+(240)/(x^2)-(32)/(x^5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (3x^2-2/x)^5

expand

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

243 x^{10} - 810 x^{7} + 1080 x^{4} - 720 x + \frac{240}{x ^{2}} - \frac{32}{x ^{5}}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

\frac{5 !}{0 ! ( 5 - 0 ) !} (3 x^{2})^{5} (- \frac{2}{x})^{0} : 243 x^{10}

Simplify

\frac{5 !}{1 ! ( 5 - 1 ) !} (3 x^{2})^{4} (- \frac{2}{x})^{1} : - 810 x^{7}

Simplify

\frac{5 !}{2 ! ( 5 - 2 ) !} (3 x^{2})^{3} (- \frac{2}{x})^{2} : 1080 x^{4}

Simplify

\frac{5 !}{3 ! ( 5 - 3 ) !} (3 x^{2})^{2} (- \frac{2}{x})^{3} : - 720 x

Simplify

\frac{5 !}{4 ! ( 5 - 4 ) !} (3 x^{2})^{1} (- \frac{2}{x})^{4} : \frac{240}{x ^{2}}

Simplify

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

= 243 x^{10} - 810 x^{7} + 1080 x^{4} - 720 x + \frac{240}{x ^{2}} - \frac{32}{x ^{5}}

(- 1 + \frac{4 i}{n})^{2}

(6 - x)^{2}

e^{x} (e^{x} + x e^{x})

(2 + \frac{3}{x ^{2}})^{4}

(2 - x) (2 + x)

What is expand (3x^2-2/x)^5 ?
The solution to expand (3x^2-2/x)^5 is 243x^{10}-810x^7+1080x^4-720x+(240)/(x^2)-(32)/(x^5)