Question

The value of $(a^2+b^2)+(a\omega +b{\omega }^2{)}^2+(a{\omega }^2+b\omega {)}^2$ is :

• A. $4ab$
• B. $3ab$
• C. $12ab$
• D. $ab$

Answer 1

The correct option is A $4ab$

$(a^2+b^2)+(a\omega +b{\omega }^2{)}^2+(a{\omega }^2+b\omega {)}^2$
$=a^2+b^2+a^2{\omega }^2+b^2\omega +2ab+a^2\omega +b^2{\omega }^2+2ab$
$=a^2(1+{\omega }^2+\omega )+b^2(1+\omega +{\omega }^2)+4ab$

$=4ab$