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AP EAMCET202119 Aug 2021Evening ShiftMathematicsDeterminantsActual

The value of b + c a a b c + a b c c a + b is

Options

  1. Aa b c
  2. B( a + b ) ( b + c ) ( c + a )
  3. C4 a b c
  4. D( a − b ) ( b − c ) ( c − a )

Correct answer

C. 4 a b c

Step-by-step solution

Let △ = b + c a a b c + a b c c a + b . Applying R 1 → R 1 + R 2 + R 3 △ = b + c + b + c a + c + a + c a + b + a + b b c + a b c c a + b ⇒ △ = 2 b + c 2 a + c 2 a + b b c + a b c c a + b ⇒ △ = 2 b + c a + c a + b b c + a b c c a + b Applying R 1 → R 1 - R 2 ⇒ △ = 2 b + c - b a + c - ( c + a ) a + b - b b c + a b c c a + b ⇒ △ = 2 c 0 a b c + a b c c a + b Applying R 3 → R 3 - R 1 ⇒ △ = 2 c 0 a b c + a b 0 c b Applying R 2 &#85

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