Question

The value of \[ \left| \begin{array}{ccc} (a+1)^2 & (b+1)^2 & (c+1)^2 (a-1)^2 & (b-1)^2 & (c-1)^2 \end{array} \right| \] is:

• A. \( 3 \quad \left| \begin{array}{ccc} a^2 & b^2 & c^2 1 & 1 & 1 \end{array} \right| \)
• B. \( 4 \quad \left| \begin{array}{ccc} a^2 & b^2 & c^2 1 & 1 & 1 \end{array} \right| \)
• C. \( 2 \quad \left| \begin{array}{ccc} a^2 & b^2 & c^2 1 & 1 & 1 \end{array} \right| \)
• D. None of these

Hint:

In a determinant with two rows having similar terms, factor them out and simplify before calculating the determinant.

Answer 1

The Correct Option is B