Factorize: `a^2+b^2+2(a b+b c+c a)`

factorize : a^2+2ab +b^2-9c^2

Factorize: a^(2)-b^(2)+2bc-c^(2)

factorize : 108a^2-3(b-c)^2

Factorize: a^(2)+2ab+b^(2)-c^(2)

Factorize: (a-b+c)^(2)+(b-c+a)^(2)+2(a-b+c)(b-c+a)

Factorize : (a^(2)-b^(2))^(3)+(b^(2)-c^(2))^(3)+(c^(2)-a^(2))^(3)

The expression (a-b)^(3)+(b-c)^(3)+(c-a)^(3) can be factorized as (a)(a-b)(b-c)(c-a)(b)3(a-b)(b-c)(c-a)(c)-3(a-b)(b-c)(c-a)(d)(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)