Find the value of $(25 a^{2} + 16 b^{2} + 9 + 40 a b - 24 b - 30 a)$ at $a = - 1$ and $b = 2$

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Solution

The correct option is A $0$
${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
$25 a^{2} + 16 b^{2} + 9 + 40 a b - 24 b - 30 a = {(5 a)}^{2} + {(4 b)}^{2} + {(- 3)}^{2} + 2 \times 5 a \times 4 b + 2 \times 4 b \times (- 3) + 2 \times 5 a \times (- 3)$
$= {(5 a + 4 b - 3)}^{2}$
$∴$ Required value $== {(5 \times (- 1) + 4 \times 2 - 3)}^{2}$
$= {(- 5 + 8 - 3)}^{2} = {(- 8 + 8)}^{2} = 0$

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