The value of the determinant $\left|\begin{array}{lll}a^2 & a & 1 \\ b^2 & b & 1 \\ c^2 & c & 1\end{array}\right|$ is:

$(a-b)(b-c)(a-c)$

The correct answer is Option (3) → $(a-b)(b-c)(a-c)$

$Δ=\left|\begin{array}{lll}a^2 & a & 1 \\ b^2 & b & 1 \\ c^2 & c & 1\end{array}\right|$

$R_3→R_3-R_2,R_2→R_2-R_1$

$\begin{vmatrix}a^2&a&1\\b^2-a^2&b-a&0\\c^2-b^2&c-b&0\end{vmatrix}$

$=(b^2-a^2)(c-b)-(c^2-b^2)(b-a)$

$(a^2-b^2)(b-c)-(a-b)(b^2-c^2)$

$-(a-b)(b-c)(-(a+b)+(b+c))$

$(a-b)(b-c)(a-c)$