Factorise : a² + b² - 2 (ab - ac + bc)

Hi!

The given expression is a ² + b ² – 2(ab – ac + bc ).

a ² + b ² – 2(ab – ac + bc ).

= a ² + b ² – 2ab + 2ac –2bc

= (a – b)² + 2c (a – b)

= (a – b)[ (a – b) + 2c ]

= (a – b) (a – b + 2c )

Thus, a ² + b ² – 2(ab – ac + bc ) = (a – b) (a – b + 2c )

Cheers!