Question

Factorise -
(1) x^2 - 1-2a-a^2
(2) 1+2ab -(a^2+b^2)

Answer 1

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

1+2ab-a^2-b^2

= 1-(a^2+b^2-2ab)

= 1^2-(a-b)^2

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

Answer 2

$\bold{\huge{\mathfrak{\pink{Solution}}}}$

$\boxed{FACTORISE -}$

(1)

${x}^{2} - 1 - 2a - {a}^{2}$

$= {x}^{2} - (1 + 2a + {a}^{2} )$

$= {x}^{2} - (1 + a)^{2}$

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

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

(2)

$1 + 2ab - ( {a}^{2} + {b}^{2} )$

$= 1 - ( {a}^{2} + {b}^{2} - 2ab)$

$= {1}^{2} - (a - b)^{2}$

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

$(1 - a + b)(1 + a + b)$