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

The solution to expand (2a-1/b)^4 is 16a^4-(32a^3)/b+(24a^2)/(b^2)-(8a)/(b^3)+1/(b^4)

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expand (2a-1/b)^4

expand

(2 a - \frac{1}{b})^{4}

16 a^{4} - \frac{32 a ^{3}}{b} + \frac{24 a ^{2}}{b ^{2}} - \frac{8 a}{b ^{3}} + \frac{1}{b ^{4}}

Solution steps

(2 a - \frac{1}{b})^{4}

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

= 16 a^{4} - \frac{32 a ^{3}}{b} + \frac{24 a ^{2}}{b ^{2}} - \frac{8 a}{b ^{3}} + \frac{1}{b ^{4}}

\frac{6 ( s + 2 )}{( s + 1 ) ( s + 3 ) ( s + 4 )}

(x + 5 - 1)^{2}

\frac{s ^{2} + s + 3}{( s - 1 ) ( s + 2 ) ( s + 3 )}

1 - cos (2 x)

2 (1 - cos (θ))

What is expand (2a-1/b)^4 ?
The solution to expand (2a-1/b)^4 is 16a^4-(32a^3)/b+(24a^2)/(b^2)-(8a)/(b^3)+1/(b^4)