Question

Expand: ${(-a+b-c)}^2$

Answer 1

Using the identity is $(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca$.

Consider ${(-a+b-c)}^2$ we apply the above identity as follows:

${\left(\right(-a)+b+(-c\left)\right)}^2={(-a)}^2+{\left(b\right)}^2+{(-c)}^2+(2\times -a\times b)+(2\times b\times -c)+(2\times -c\times -a)$

$=a^2+b^2+c^2-2ab-2bc+2ca$

Hence, ${(-a+b-c)}^2=a^2+b^2+c^2-2ab-2bc+2ca$.