Question

 \(\frac{\left(x-y\right)^3-3xy\left(x+y\right)+y^3}{x-6y}\)

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Answer 1

\(\frac{\left(x-y\right)^3-3xy\left(x+y\right)+y^3}{x-6y}\)

\(=\frac{x^3-3x^2y+3xy^2-y^3-3x^2y-3xy^2+y^3}{x-6y}\)

\(=\frac{x^3-6x^2y}{x-6y}\)

\(=\frac{x^2\left(x-6y\right)}{x-6y}\)

\(=x^2\)

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Answer 2

(x-y)³ - 3xy(x+y) + y³

x - 6y

x³ - 3x²y +3xy² - y³ - 3x²y - 3xy² + y³

x - 6y

x³ - 6x²y

x - 6y

x²(x-6y)

x - 6y

= x²