Question

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

Answer 1

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Q. Factorize 1 + 2 ab - ( a² + b² )


Sol : 1 + 2 ab - ( a² + b² )

    = 1 + 2 ab - a² - b²

    = 1 - ( a² + b² - 2 ab )

We know that ( a² + b² - 2 ab ) = ( a - b )².

By putting the value of ( a² + b² - 2 ab ) in above equation,

    = 1 - ( a - b )²

   = ( 1 )² - ( a - b )²

Let , 1 = A and ( a - b ) = B.

  = A² - B²

  = ( A + B ) ( A - B )

By putting back the value of value of A and B in above equation,

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


    = ( 1 + a - b ) ( 1 - a + b )

            
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Answer 2

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

hope this helped u