Question

Factorise using identity
$x - y - {x}^{2} + {y}^{2}$
​

Answer 1

$\LARGE{ \underline{ \green{ \sf{Required \: answer:}}}}$

We have to factorise:

• x - y - x² + y²

Let's factorise by using identity within the terms to get the simplified value of the given polynomial. It can written as:

⇛ x - y - (x² - y²)

Here, we can use the identity of x² - y² = (x + y)(x - y),

⇛ (x - y) - (x + y)(x - y)

In the both sides of the '-' minus signs, (x - y) is common. So, we take it common to factorise more.

⇛ (x - y){1 - (x + y)}

This is equals to,

⇛ (x - y)(1 - x - y)

And we are done factorising the above polynomial...(Ans - (x - y)(1 - x - y)

Answer 2

$\LARGE{ \underline{ \underline{ \bf{ \purple{Required \: Answer:}}}}}$

We have to factorise:

x - y - x² + y²

Let's factorise by using identity within the terms to get the simplified value of the given polynomial. It can written as:

⇛ x - y - (x² - y²)

Here, we can use the identity of x² - y² = (x + y)(x - y),

⇛ (x - y) - (x + y)(x - y)

In the both sides of the '-' minus signs, (x - y) is common. So, we take it common to factorise more.

⇛ (x - y){1 - (x + y)}

This is equals to,

⇛ (x - y)(1 - x - y)

And we are done factorising the above polynomial...(Ans - (x - y)(1 - x - y)