Factorise:
25a² − 4b² + 28bc − 49c²

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Solution

We have:
$25 a^{2} - 4 b^{2} + 28 b c - 49 c^{2} = 25 a^{2} - (4 b^{2} - 28 b c + 49 c^{2})$
$= {(5 a)}^{2} - {(2 b - 7 c)}^{2} = \{5 a + (2 b - 7 c)\} \{5 a - (2 b - 7 c)\} = (5 a + 2 b - 7 c) (5 a - 2 b + 7 c)$

∴ $25 a^{2} - 4 b^{2} + 28 b c - 49 c^{2} = (5 a + 2 b - 7 c) (5 a - 2 b + 7 c)$

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

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

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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