Question

(x+y)(x-xy+y)+(x-y)(x+xy+y)

Answer 1

Ответ:

$2x^{2}+2xy-2xy^{2}=2x(x+y-y^{2}).$

Пошаговое объяснение:

$(x+y)(x-xy+y)+(x-y)(x+xy+y);\\1)(x+y)(x-xy+y)=x^{2}-x^{2}y+xy+xy-xy^{2}+y^{2}=\\=x^{2}-x^{2}y+2xy-xy^{2}+y^{2}\\2)(x-y)(x+xy+y)=x^{2}+x^{2}y+xy-xy-xy^{2}-y^{2}=\\=x^{2}+x^{2}y-xy^{2}-y^{2}\\3)x^{2}+x^{2}-x^{2}y+x^{2}y+2xy-xy^{2}-xy^{2}-y^{2}+y^{2}=2x^{2}+2xy-2xy^{2}$

Answer 2

To simplify the given expression, let's work step by step:

Given expression:

$(x+y)(x-xy+y) + (x-y)(x+xy+y)$

Let's first simplify each term within the parentheses:

For the first term: $(x+y)(x-xy+y)$

Expand the first term: $x(x) + x(-xy) + x(y) + y(x) + y(-xy) + y(y)$

Simplify: $x^2 - x^2y + xy + xy - xy^2 + y^2$

Combine like terms: $x^2 + 2xy - x^2y - xy^2 + y^2$

For the second term: $(x-y)(x+xy+y)$

Expand the second term: $x(x) + x(xy) + x(y) - y(x) - y(xy) - y(y)$

Simplify: $x^2 + x^2y + xy - xy - xy^2 - y^2$

Combine like terms: $x^2 + x^2y - xy^2 - y^2$

Now we have:

$(x^2 + 2xy - x^2y - xy^2 + y^2) + (x^2 + x^2y - xy^2 - y^2)$

Combine the terms from both parentheses:

$x^2 + 2xy - x^2y - xy^2 + y^2 + x^2 + x^2y - xy^2 - y^2$

Simplify by combining like terms:

$2x^2 + 2xy - 2xy^2$

Finally, factor out common terms:

$2x^2 + 2xy(1 - y)$

So, the simplified expression is:

$2x^2 + 2xy(1 - y)$