What is expand (2x-1/x)^4 ?

The solution to expand (2x-1/x)^4 is 16x^4-32x^2+24-8/(x^2)+1/(x^4)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (2x-1/x)^4

expand

(2 x - \frac{1}{x})^{4}

16 x^{4} - 32 x^{2} + 24 - \frac{8}{x ^{2}} + \frac{1}{x ^{4}}

Solution steps

(2 x - \frac{1}{x})^{4}

Apply binomial theorem:

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

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

= i = 0 \sum 4 (i 4) (2 x)^{(4 - i)} (- \frac{1}{x})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (2 x)^{4} (- \frac{1}{x})^{0} : 16 x^{4}

Simplify

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

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (2 x)^{2} (- \frac{1}{x})^{2} : 24

Simplify

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

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (2 x)^{0} (- \frac{1}{x})^{4} : \frac{1}{x ^{4}}

= 16 x^{4} - 32 x^{2} + 24 - \frac{8}{x ^{2}} + \frac{1}{x ^{4}}

(x + y) d x

\frac{1}{( s - 1 ) ^{2}}

(2 t - 3) e^{\frac{t + 2}{3}}

\frac{s ^{2} + 1}{s ^{2} ( s + 2 )}

(3 + 4 i)^{4}

What is expand (2x-1/x)^4 ?
The solution to expand (2x-1/x)^4 is 16x^4-32x^2+24-8/(x^2)+1/(x^4)