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

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

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expand (2x-1/y)^4

expand

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

16 x^{4} - \frac{32 x ^{3}}{y} + \frac{24 x ^{2}}{y ^{2}} - \frac{8 x}{y ^{3}} + \frac{1}{y ^{4}}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

Simplify

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

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

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