Question

Question :

Factorise

(1) x^2 - 1 -2a - a^2

(2) 1 + 2ab - ( a^2 + b^2 )​

Answer 1

Answer:

(1). ( x - 1 - a ) ( x + 1 + a ).

(2). ( 1 - a + b ) ( 1 + a -b ).

Step-by-step explanation:

Factorise :

(1). x² - 1 - 2a - a²

(2). 1 + 2ab - (a² + b²)

Solution :

We have

(1). x² - 1 - 2a - a²

= x² - ( 1 + 2a + a² )

= x² - ( 1 + a )²

= {x-( 1 + a )} { x + ( 1 + a )}

[ ∵ (a² - b²) = (a + b) (a - b)]

= ( x - 1 - a ) ( a + 1 + a).

= ∴ ( x² - 1 - 2a - a² )

= ( x - 1 - a ) ( x + 1 + a ).

(2) 1 + 2ab - ( a² + b²)

= 1 - ( a² + b² - 2ab )

= 1² - ( a - b )²

= {1 - (a + b)} {1+ (a-b}

[ ∵ ( a²+b²)

= (a+b) (a-b)= ( 1 - a + b ) (1 + a- b)

= ∴ 1 + 2ab - ( a² + b² )

= ( 1 - a + b ) ( 1 + a -b )