What is expand (3sqrt(x)-2/(sqrt(x)))^4 ?

The solution to expand (3sqrt(x)-2/(sqrt(x)))^4 is 81x^2-216x+216-(96)/x+(16)/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand (3sqrt(x)-2/(sqrt(x)))^4

expand

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

81 x^{2} - 216 x + 216 - \frac{96}{x} + \frac{16}{x ^{2}}

Solution steps

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

Apply binomial theorem:

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

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

= i = 0 \sum 4 (i 4) (3 x)^{(4 - i)} (- \frac{2}{x})^{i}

Expand summation

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

Simplify

\frac{4 !}{0 ! ( 4 - 0 ) !} (3 x)^{4} (- \frac{2}{x})^{0} : 81 x^{2}

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} (3 x)^{3} (- \frac{2}{x})^{1} : - \frac{216 ( x ) ^{3}}{x}

Simplify

\frac{4 !}{2 ! ( 4 - 2 ) !} (3 x)^{2} (- \frac{2}{x})^{2} : 216

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} (3 x)^{1} (- \frac{2}{x})^{3} : - \frac{96 x}{( x ) ^{3}}

Simplify

\frac{4 !}{4 ! ( 4 - 4 ) !} (3 x)^{0} (- \frac{2}{x})^{4} : \frac{16}{x ^{2}}

= 81 x^{2} - \frac{216 ( x ) ^{3}}{x} + 216 - \frac{96 x}{( x ) ^{3}} + \frac{16}{x ^{2}}

Simplify

81 x^{2} - \frac{216 ( x ) ^{3}}{x} + 216 - \frac{96 x}{( x ) ^{3}} + \frac{16}{x ^{2}} : 81 x^{2} - 216 x + 216 - \frac{96}{x} + \frac{16}{x ^{2}}

= 81 x^{2} - 216 x + 216 - \frac{96}{x} + \frac{16}{x ^{2}}

\frac{( x - 8 ) ^{2}}{( x ^{2} - 16 )}

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

\frac{x ( x - 1 ) ( x - 2 ) ( x - 3 )}{24}

lo g_{10} (2) (x + 2)

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

What is expand (3sqrt(x)-2/(sqrt(x)))^4 ?
The solution to expand (3sqrt(x)-2/(sqrt(x)))^4 is 81x^2-216x+216-(96)/x+(16)/(x^2)