Factorise: $25 a^{2} + b^{2} - 100 a b - 49$

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Solution

Given that

$25 a^{2} + b^{2} - 10 a b - 49$

= ${(5 a)}^{2} + b^{2} - 10 (5 a - b)$

= ${(5 a - b)}^{2} - 7^{2}$

= $(5 a - b - 7) (5 a - b + 7)$

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

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