When $5 a^{2} b + 10 b^{2} c^{2} - 21 a b + 32$ is subtracted from $50 - 20 b^{2} c^{2} - 4 b c - a c - 5 a b$ , we get

$18 + 30 b^{2} c^{2} - 4 b c - a c + 16 a b - 5 a^{2} b + 10 b^{2} c$

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$18 - 30 b^{2} c^{2} - 4 b c - a c + 16 a b - 5 a^{2} b$

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$20 - 30 b^{2} c^{2} - 4 b c - a c + 16 a b - 5 a^{2} b$

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$22 - 30 b^{2} c^{2} - 4 b c - a c - 16 a b - 5 a^{2} b$

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Solution

The correct option is B: $18 - 30 b^{2} c^{2} - 4 b c - a c + 16 a b - 5 a^{2} b$
We have
$(50 - 20 b^{2} c^{2} - 4 b c - a c - 5 a b) - (5 a^{2} b + 10 b^{2} c^{2} - 21 a b + 32)$

$= 50 - 20 b^{2} c^{2} - 4 b c - a c - 5 a b - 5 a^{2} b - 10 b^{2} c^{2} + 21 a b - 32$
$= 50 - 32 - 20 b^{2} c^{2} - 10 b^{2} c^{2} - a c - 4 b c - 5 a^{2} b + 21 a b - 5 a b$

$= 18 - 30 b^{2} c^{2} - a c - 4 b c - 5 a^{2} b + 16 a b$
$= 18 - 30 b^{2} c^{2} - 4 b c - a c + 16 a b - 5 a^{2} b$

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When 5a2b+10b2c2−21ab+32 is subtracted from 50−20b2c2−4bc−ac−5ab, we get

When $5 a^{2} b + 10 b^{2} c^{2} - 21 a b + 32$ is subtracted from $50 - 20 b^{2} c^{2} - 4 b c - a c - 5 a b$ , we get