What is expand ((x-y)^2)/(4x^6) ?

The solution to expand ((x-y)^2)/(4x^6) is 1/(4x^4)-y/(2x^5)+(y^2)/(4x^6)

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expand ((x-y)^2)/(4x^6)

expand

\frac{( x - y ) ^{2}}{4 x ^{6}}

\frac{1}{4 x ^{4}} - \frac{y}{2 x ^{5}} + \frac{y ^{2}}{4 x ^{6}}

Solution steps

\frac{( x - y ) ^{2}}{4 x ^{6}}

(x - y)^{2} = x^{2} - 2 x y + y^{2}

= \frac{x ^{2} - 2 x y + y ^{2}}{4 x ^{6}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{2} - 2 x y + y ^{2}}{4 x ^{6}} = \frac{x ^{2}}{4 x ^{6}} - \frac{2 x y}{4 x ^{6}} + \frac{y ^{2}}{4 x ^{6}}

= \frac{x ^{2}}{4 x ^{6}} - \frac{2 x y}{4 x ^{6}} + \frac{y ^{2}}{4 x ^{6}}

Cancel

\frac{x ^{2}}{4 x ^{6}} : \frac{1}{4 x ^{4}}

= \frac{1}{4 x ^{4}} - \frac{2 x y}{4 x ^{6}} + \frac{y ^{2}}{4 x ^{6}}

Cancel

\frac{2 x y}{4 x ^{6}} : \frac{y}{2 x ^{5}}

= \frac{1}{4 x ^{4}} - \frac{y}{2 x ^{5}} + \frac{y ^{2}}{4 x ^{6}}

(1 - \frac{x}{3} = \frac{5 x}{3}) 3

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What is expand ((x-y)^2)/(4x^6) ?
The solution to expand ((x-y)^2)/(4x^6) is 1/(4x^4)-y/(2x^5)+(y^2)/(4x^6)