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

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Solution

$25 a^{2} - 4 b^{2} + 28 b c - 49 c^{2} = 25 a^{2} - [4 b^{2} + 28 b c - 49 c^{2}] {∵ a^{2} - 2 a b + b^{2} = (a - b)^{2}} = (5 a)^{2} - [(2 b)^{2} - 2 \times 2 b \times 7 c + (7 c)^{2}] = (5 a)^{2} - (2 b - 7 c)^{2} {a^{2} - b^{2} = (a + b) (a - b)} = (5 a + 2 b - 7 c) (5 a - 2 b + 7 c)$

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

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

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

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

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

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