Question

The value of the determinant $\left|\begin{array}{ccc}a& b& c\\ a^2& b^2& c^2\\ bc& ca& ab\end{array}\right|$ is

• A. $abc\left(ab\right)\left(bc\right)\left(ca\right)$
• B. $(a+b)\left(bc\right)\left(ca\right)(a+b+c)$
• C. $\left(ab\right)\left(bc\right)\left(ca\right)(ab+bc+ca)$
• D. none

Answer 1

The correct option is D none

$\left|\begin{array}{ccc}a& b& c\\ a^2& b^2& c^2\\ bc& ca& ab\end{array}\right|$

$a(b^{3}a-c^{3}a)-b(a^{3}b-c^{3}b)+c(a^{3}c-b^{3}c)$

$\Rightarrow a^2{b}^3-a^2{c}^3-a^3{b}^2+c^3{b}^2+a^3{c}^2-b^3{c}^2$

$\Rightarrow a^2{b}^2(b-a)+a^2{c}^2(a-c)+b^2{c}^2(c-b)$

Option D-none