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(x^(3)-3x^(2)y+3xy^(2)-y^(3))/(x^(3)-y^(3))

x3−3x2y+3xy2−y3x3−y3 \frac{x^{3}-3 x^{2} y+3 x y^{2}-y^{3}}{x^{3}-y^{3}}

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Find derivatives of using multiple formulaeright chevron icon

Full solution

Q. x3−3x2y+3xy2−y3x3−y3 \frac{x^{3}-3 x^{2} y+3 x y^{2}-y^{3}}{x^{3}-y^{3}}
  1. Recognize: Recognize the numerator as a cubic polynomial and the denominator as a difference of cubes.\newlineNumerator: x3−3x2y+3xy2−y3x^3 - 3x^2y + 3xy^2 - y^3\newlineDenominator: x3−y3x^3 - y^3
  2. Factorize: Factorize the numerator and denominator.\newlineNumerator: (x−y)3(x - y)^3 (using the formula a3−3a2b+3ab2−b3=(a−b)3a^3 - 3a^2b + 3ab^2 - b^3 = (a - b)^3)\newlineDenominator: (x−y)(x2+xy+y2)(x - y)(x^2 + xy + y^2) (using the formula a3−b3=(a−b)(a2+ab+b2)a^3 - b^3 = (a - b)(a^2 + ab + b^2))
  3. Simplify: Simplify the expression by canceling out common factors.\newline(x−y)3/(x−y)(x2+xy+y2)=(x−y)2/(x2+xy+y2)(x - y)^3 / (x - y)(x^2 + xy + y^2) = (x - y)^2 / (x^2 + xy + y^2)

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