Question

Evaluate the determinant:
\[ \left| \begin{array}{ccc} b+c & a-b & a\\ c+a & b-c & b\\ a+b & c-a & c\\ \end{array} \right| \]

• A. \(3abc-a^3-b^3-c^3\)
• B. \(3abc+a^3+b^3+c^3\)
• C. \(3abc-a^3+b^3-c^3\)
• D. \(3abc+a^3-b^3-c^3\)

Hint:

For a \(3\times 3\) determinant, expand carefully along any row or column and simplify term by term. Always keep track of signs \(+,-,+\).

Answer 1

The Correct Option is A