Question

Simplify: (a+b+c)²+(a-b+c)²+(a+b-c)²​

Answer 1

Answer:

3(a²+b²+c²)+2(ab+ac-bc)

Step-by-step explanation:

(a+b+c)²+(a-b+c)²+(a+b-c)²​

= (a+b)² + 2c(a+b) + c² + (a-b)² + 2c(a-b) +c²+(a+b)²-2c(a+b)+c²

=2(a+b)²+(a-b)²+2c(a-b) + 3c²

=2(a²+2ab+b²) + (a²-2ab+b²) +2ac-2bc + 3c²

=2a²+4ab+2b²+a²-2ab+b²+2ac-2bc + 3c²

=3a²+2ab+3b²+2ac-2bc+3c²

=3(a²+b²+c²)+2(ab+ac-bc)