Question

simplify x cube + y cube by x square minus y square

Answer 1

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Answer 2

Solution :

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Given :

To find the value of :

⇒ $\frac{x^3 + y^3}{x^2 - y^2}$

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We know that,

x³ + y³ = (x + y)(x² + xy + y²)

&

x² - y² = (x + y)(x - y)
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So,


⇒ $\frac{x^3 + y^3}{x^2 - y^2}$

⇒ $\frac{(x + y)(x^2 - xy + y^{2} )}{(x + y)(x - y)}$

⇒ $\frac{ x^{2} - xy + y^2}{ x - y}$

⇒ $\frac{x^2 - xy + y^2 - xy + xy}{x - y}$   (By adding & subtracting xy, for further simplification)

⇒ $\frac{x^2 - 2xy + y^2 + xy}{x - y}$

⇒ $\frac{(x - y)^2 + xy}{x - y}$

⇒ $\frac{(x - y)^2}{x - y} + \frac{xy}{x - y}$

⇒ $\frac{(x - y)(x - y)}{x - y} + \frac{xy}{x - y}$

⇒ $x - y + \frac{xy}{x - y}$

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                                        Hope it Helps !!