Question

Expand $(a-b-c{)}^2$ using expansion formula $(a+b+c{)}^2$.

• A. $a^2+b^2+c^2+2ab-2bc+2ac$
• B. $a^2+b^2+c^2+2ab+2bc+2ac$
• C. $a^2+b^2+c^2-2ab+2bc-2ac$
• D. $a^2+b^2+c^2-2ab-2bc-2ac$

Answer 1

The correct option is C $a^2+b^2+c^2-2ab+2bc-2ac$

Given expression: $(a-b-c{)}^2$
We can write $(a-b-c{)}^2$ as $[a+(-b)+(-c){]}^2$ which is in the form of $(a+b+c{)}^2$.
$a=a;b=(-b);$ and $c=(-c)$
We know that
$(a+b+c{)}^2=a^2+b^2+c^2$
$+2ab+2bc+2ac$

$\Rightarrow$ $(a-b-c{)}^2$
$=a^2+(-b{)}^2+(-c{)}^2+2a(-b)$
$+2(-b)(-c)+2\left(a\right)(-c)$
$=a^2+b^2+c^2-2ab+2bc-2ac$