Question

The value of $(x-a{)}^3+(x-b{)}^3+(x-c{)}^3-3(x-a\left)\right(x-b\left)\right(x-c)$ when $a+b+c=3x$, is ____

• A. 3
• B. 2
• C. 1
• D. 0

Answer 1

The correct option is D 0

we know that,

$a^3+b^3+c^3=(a+b+c)(a^2+b^2+c^2-ab-bc-ac)$

if a+b+c=0 then,

$a^3+b^3+c^3-3abc=0\times (a^2+b^2+c^2-ab-bc-ca)=0-\left(1\right)$

$(x-a{)}^3+(x-b{)}^3+(x-c{)}^3-3(x-a\left)\right(x-b\left)\right(x-c)$

let $a=(x-a)$

$b=(x-b)$

and $c=(x-c)$

$a+b+c=x-a+x-b+x-c=3x-(a+b+c)=3x-3x=0.$...(as $a+b+c=3x)$

$(x-a{)}^3+(x-b{)}^3+(x-c{)}^3-3(x-a\left)\right(x-b\left)\right(x-c)=0$

Thus the answer is 0.