Mark the correct alternative in the following question:

What should be added to xy + yz + zx to get $-$ xy $-$ yz $-$ zx?

(a) $-$ 2xy $-$ 2yz $-$ 2zx (b) $-$ 3xy $-$ yz $-$ zx (c) $-$ 3xy $-$ 3yz $-$ 3zx (d) 2xy + 2yz + 2zx

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Solution

Since, ( $-$ xy $-$ yz $-$ zx) $-$ (xy + yz + zx) = $-$ xy $-$ yz $-$ zx $-$ xy $-$ yz $-$ zx = $-$ 2xy $-$ 2yz $-$ 2zx

So, $-$ 2xy $-$ 2yz $-$ 2zx should be added to xy + yz + zx to get $-$ xy $-$ yz $-$ zx.

Hence, the correct alternative is option (a).

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