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Multiplication of a Binomial by a Binomial

Simplify.x2+y...

Question

Simplify. $(x^{2} + y^{2} - 3 x y) - (y^{2} - 4 x y - 3 x^{2})$

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Solution

Simplification of Given Equation
$(x^{2} + y^{2} - 3 x y) - (y^{2} - 4 x y - 3 x^{2}) = x^{2} + y^{2} - 3 x y - y^{2} + 4 x y + 3 x^{2}$ {After removing the bracket the sign of second bracket change}
$(x^{2} + y^{2} - 3 x y) - (y^{2} - 4 x y - 3 x^{2}) = x^{2} + 3 x^{2} + y^{2} - y^{2} - 3 x y z + 4 x y = 4 x^{2} + x y$
$∴ (x^{2} + y^{2} - 3 x y) - (y^{2} - 4 x y - 3 x^{2}) = 4 x^{2} + x y$ .

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[\frac{x^{3} + y^{3}}{(x - y)^{2} + 3 x y}] + [\frac{(x + y)^{2} - 3 x y}{x^{3} - y^{3}}] \times \frac{x y}{x^{2} - y^{2}}

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[\frac{x^{3} + y^{3}}{{(x - y)}^{2} + 3 x y}] \div [\frac{{(x + y)}^{2} - 3 x y}{x^{3} - y^{3}}] \times \frac{x y}{x^{2} - y^{2}}

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