Factorise: 25a^2– 4b^2+ 28bc – 49c^2 - Vidyadip

Question

Factorise: $25a^2– 4b^2+ 28bc – 49c^2$

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Answer

$25a^2– 4b^2+ 28bc – 49c^2$
$= 25a^2– (4b^2– 28bc + 49c^2)$
$= 25a^2– {(2b)^2– 2(2b) (7c) + (7c)^2}$
$= (5a)^2– (2b – 7c)^2. . . .$ [Using Identity $II$
$= {5a – (2b – 7c)} {5a + (2b – 7c)}$
$= (5a – 2b + 7c) (5a + 2b – 7c)$

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