Question

Find the parity of the following if a and b have different parities. (5a - 3b)(a² + 5b) + 2

Answer 1

9514 1404 393

Answer:

  odd

Step-by-step explanation:

If 'a' and 'b' have different parity, the result has odd parity.

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Assume a=odd, b=even

  (5·odd -3·even) = odd

  (odd^2 +5·even) = odd

  (odd)(odd) +2 = odd

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Assume a=even, b=odd

  (5·even -3·odd) = odd

  (even^2 +5(odd)) - odd

  (odd)(odd) +2 = odd

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The attached verifies this with numbers.