Factorize a^2+b^2+2 (ab-ac-bc)

(a + b) (a + b - 2c)

Step-by-step explanation:

Note that

(a + b) ² = a² + b² + 2ab

Given

a² + b² + 2 (ab - ac - bc) ← distribute parenthesis

= a² + b² + 2ab - 2ac - 2bc

= (a + b) ² - 2ac - 2bc ← factor out - 2c from each term

= (a + b) ² - 2c (a + b) ← factor out (a + b) from each term

= (a + b) [ a + b - 2c ]

= (a + b) (a + b - 2c) ← in factored form