Subtract the sum of ${9 b}^{2} + {3 c}^{2}$ and ${2 b}^{2} + b c + {2 c}^{2}$ from the sum of ${2 b}^{2} - 2 b c - c^{2}$ and $c^{2} + 2 b c - b^{2}$ .

{13 b}^{2} - 5 b c + {5 c}^{2}

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{- 10 b}^{2} - b c - {5 c}^{2}

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{10 b}^{2} + b c - {5 c}^{2}

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{- 10 b}^{2} - 5 b c - {5 c}^{2}

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Solution

The correct option is B ${- 10 b}^{2} - b c - {5 c}^{2}$
According to the question,
${({2 b}^{2} - 2 b c - c^{2}) + (c^{2} + 2 b c - b^{2})} - {({9 b}^{2} + {3 c}^{2}) + ({2 b}^{2} + b c + {2 c}^{2})}$
= ${({2 b}^{2} - b^{2}) + (- 2 b c + 2 b c) + (c^{2} - c^{2})} - {({9 b}^{2} + {2 b}^{2}) + ({3 c}^{2} + {2 c}^{2}) + b c}$
$= (b^{2}) - ({11 b}^{2} + {5 c}^{2} + b c)$
$= b^{2} - {11 b}^{2} - {5 c}^{2} - b c$
$= - {10 b}^{2} - b c - {5 c}^{2}$ .

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Question 71

Subtract the sum of $12 a b - 10 b^{2} - 18 a^{2}$ and $9 a b + 12 b^{2} + 14 a^{2}$ from the sum of $a b + 2 b^{2}$ and $3 b^{2} - a^{2} .$

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