Question

Factorise 1 – x2 + 2xy – y2 plz write with steps

Answer 1

hey mate here's ur answer

1 - x² + 2xy - y²

= 1 - (x² - 2xy + y²)

using identity

(a-b)² = a² - 2ab + b²

= 1 - (x - y)²

= 1² - (x-y)²

using identity

a²-b² = (a-b)(a+b)

= [ 1 - (x-y)] [1 + (x-y)]

( 1 - x + y) ( 1 + x - y)

Answer 2

Answer:

(1 + x - y) (1 - x + y) is the required solution.

Step-by-step explanation:

Given polynomial is 1 - x² + 2xy - y²

We need to factorise the above.

Therefore,

Taking negative from all the terms excluding the term containing 1.

=> 1 - ( x² - 2xy + y² )

We know that (a - b)² = a² + b² - 2ab

Therefore, using this identity above, we get

1 - [(x - y)²]

This can be written as

1² - (x - y)²

We also know that (a + b) (a - b) = a² - b²

Therefore, using this, we get,

(1 + (x-y)) (1 - (x-y))

On solving, we get

(1 + x - y) (1 - x + y)

which is the required solution.