Question

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

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Answer 1

Answer:

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

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

1+(a+b)^2

Step-by-step explanation:

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Answer 2

Answer:

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

Step-by-step 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)

∴  1-2ab-(a²+b²) = (1+a+b)(1-a-b)