Question

factorise a^2-x^2-2xy-y^2

Answer 1

Hi there !

Given,
To factorise.

a² - x² - 2xy - y²

= a² - (x² + 2xy + y²)

Using the algebraic identity , (a+b)²=a²+2ab+b²,
we have,

= a² - (x + y)²
Here
Let
x = a. b = x + y
So,
Using the identity , x² - b² = (x - b)(x + b)

we have,

a² - x² - 2xy - y² = (a - x - y)(a + x + y). [ Answer]

Answer 2

Hey!

______________

a^2 - x^2 - 2xy - y^2

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

We know, (a+b)^2 = a^2 + 2ab + b^2

a^2 - (x+y)^2

Now, let b = x+y
Using identity - a^2 - b^2 = (a+b) (a-b)

Answer - (a-x-y) (a+x+y)

______________

Hope it helps...!!!