Factorize using appropriate identities
$49 a^{2} + 70 a b + 25 b^{2}$

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Solution

We know $49 a^{2} + 70 a b + 25 b^{2}$ $= (7 a)^{2} + 2 (7 a) (5 b) + (5 b)^{2}$
We know that $x^{2} + 2 x y + y^{2} = (x + y)^{2}$
Here $x = 7 a$ and $y = 5 b$
Therefore, $49 a^{2} + 70 a b + 25 b^{2} = (7 a)^{2} + 2 (7 a) (5 b) + (5 b)^{2}$
$= (7 a + 5 b)^{2}$
$= (7 a + 5 b) (7 a + 5 b)$

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