Simplify the expression: (x^(3)+3x^(2)y+3xy^(2)+y^(3))/(x^(3)+y^(3))

Recognize Perfect Cube Formula: Recognize the numerator as a perfect cube formula: (x+y)^3 = x^3 + 3x^2y + 3xy^2 + y^3. Calculation: (x+y)^3 = x^3 + 3x^2y + 3xy^2 + y^3.Identify Sum of Cubes: Identify the denominator as a sum of cubes: x^3 + y^3 = (x + y)(x^2 - xy + y^2). Calculation: x^3 + y^3 = (x + y)(x^2 - xy + y^2).Simplify Expression: Simplify the original expression by substituting the identified forms: (x+y)^3 / (x+y)(x^2 - xy + y^2). Calculation: (x+y)^3 / (x+y)(x^2 - xy + y^2) = (x+y)^2.

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Simplify the expression: (x^(3)+3x^(2)y+3xy^(2)+y^(3))/(x^(3)+y^(3))

Simplify the expression: $\frac{x^{3}+3x^{2}y+3xy^{2}+y^{3}}{x^{3}+y^{3}}$

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Q. Simplify the expression:

\frac{x^{3}+3x^{2}y+3xy^{2}+y^{3}}{x^{3}+y^{3}}

Recognize Perfect Cube Formula: Recognize the numerator as a perfect cube formula: $x+y$ ^ $3$ = x^ $3$ + $3$ x^ $2$ y + $3$ xy^ $2$ + y^ $3$ . Calculation: $x+y$ ^ $3$ = x^ $3$ + $3$ x^ $2$ y + $3$ xy^ $2$ + y^ $3$ .
Identify Sum of Cubes: Identify the denominator as a sum of cubes: $x^3 + y^3 = (x + y)(x^2 - xy + y^2)$ . Calculation: $x^3 + y^3 = (x + y)(x^2 - xy + y^2)$ .
Simplify Expression: Simplify the original expression by substituting the identified forms: $\newline$ $(x+y)^3 / (x+y)(x^2 - xy + y^2)$ . $\newline$ Calculation: $(x+y)^3 / (x+y)(x^2 - xy + y^2) = (x+y)^2$ .