Question

a2+b2+2ab+2a+2b+1 factorise using suitable identities

Answer 1

Answer:

Factors of 1-2ab-(a²+b²)

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

Explanation:

Given 1-2ab-(a²+b²)

= 1-2ab-a²-b²

= 1-(2ab+a²+b²)

= 1-(a+b)²

/* By algebraic identity : x²+y²+2xy =(x+y)² */

= 1²-(a+b)²

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

/* By algebraic identity :

x²-y² =(x+y)(x-y) */

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

Therefore,

1-2ab-(a²+b²) = (1+a+b)(1-a-b)