Solve $16 a^{2} - 40 a b + 25 b^{2} - 9 x^{2} + 42 x - 49$

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Solution

$16 a^{2} - 40 a b + 25 b^{2} - 9 x^{2} + 42 x - 49$
$= {(4 a)}^{2} - 2.4 a .5 b + {(5 b)}^{2} - [{(3 x)}^{2} - 2.3 x .7 + 7^{2}]$
$= {(4 a - 5 b)}^{2} - {(3 x - 7)}^{2}$
$= (4 a - 5 b + 3 x - 7) (4 a - 5 b - 3 x + 7)$

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