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

Предыдущий
вопрос Следующий
вопрос

To simplify the expression (\frac{x^3-y^3-x^2y+xy^2}{(x+y)^2}-2xy), we first need to factor the numerator:

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

Now our expression becomes:

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

Next, expand the numerator:

(\frac{x^3 + x^2y + xy^2 - y^3 - x^2y - xy^2 - xy^2}{(x+y)^2} - 2xy)

(\frac{x^3 - y^3 - xy^2}{(x+y)^2} - 2xy)

Now, we know that (x^3 - y^3 = (x-y)(x^2+xy+y^2)), so we can rewrite the expression again:

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

Finally, let's expand the numerator and simplify:

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

This is the simplified form of the expression (\frac{x^3-y^3-x^2y+xy^2}{(x+y)^2}-2xy).