What is expand (x^2-2/x)^4 ?

The solution to expand (x^2-2/x)^4 is x^8-8x^5+24x^2-(32)/x+(16)/(x^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (x^2-2/x)^4

expand

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

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

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (x^{2})^{3} (- \frac{2}{x})^{1} : - 8 x^{5}

Simplify

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

Simplify

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

Simplify

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

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

(2 A x + B) e^{x} + e^{x} (A x^{2} + B x)

\frac{( 6 - x ) ^{2}}{9}

a (arctan (wT) - arctan (w Y))

a^{2} b^{2} - c^{2} d^{2} (sin (2 α) + 1)

(1 - L) \cdot (1 - t) \cdot w

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