Factorise: $25 a^{2} - 4 b^{2} + 28 b c - 49 c^{2}$

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Solution

$25 a^{2} - (4 b^{2} - 28 b c + 49 c^{2})$ splitting middle term,
$= 25 a^{2} - [4 b^{2} - 14 b c - 14 b c + 49 c^{2}]$
$= 25 a^{2} - [2 b (2 b - 7 c) - 7 c (2 b - 7 c)]$
$= 25 a^{2} - (2 b - 7 c)^{2} = (5 a)^{2} - (2 b - 7 c)^{2}$
$= (5 a + 2 b - 7 c) (5 a - 2 b + 7 c)$ .

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