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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}+3x^{2}y+3xy^{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}+3x^{2}y+3xy^{2}+y^{3}}{x^{3}+y^{3}}
  1. Recognize Perfect Cube Formula: Recognize the numerator as a perfect cube formula: x+yx+y^33 = x^33 + 33x^22y + 33xy^22 + y^33. Calculation: x+yx+y^33 = x^33 + 33x^22y + 33xy^22 + y^33.
  2. Identify Sum of Cubes: Identify the denominator as a sum of cubes: x3+y3=(x+y)(x2−xy+y2)x^3 + y^3 = (x + y)(x^2 - xy + y^2). Calculation: x3+y3=(x+y)(x2−xy+y2)x^3 + y^3 = (x + y)(x^2 - xy + y^2).
  3. Simplify Expression: Simplify the original expression by substituting the identified forms: \newline(x+y)3/(x+y)(x2−xy+y2)(x+y)^3 / (x+y)(x^2 - xy + y^2).\newlineCalculation: (x+y)3/(x+y)(x2−xy+y2)=(x+y)2(x+y)^3 / (x+y)(x^2 - xy + y^2) = (x+y)^2.

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