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

User Morgs
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1 Answer

18 votes
18 votes

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Answer:

odd

Explanation:

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

__

Assume a=odd, b=even

(5·odd -3·even) = odd

(odd^2 +5·even) = odd

(odd)(odd) +2 = odd

__

Assume a=even, b=odd

(5·even -3·odd) = odd

(even^2 +5(odd)) - odd

(odd)(odd) +2 = odd

_____

The attached verifies this with numbers.

Find the parity of the following if a and b have different parities. (5a - 3b)(a² + 5b-example-1
User Daniel Benedykt
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