Solve $4 a^{2} + 12 a b + 9 b^{2} - 25 c^{2}$ by $2 a + 3 b + 5 c$

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Solution

Now,
$4 a^{2} + 12 a b + 9 b^{2} - 25 c^{2}$
$= (2 a + 3 b)^{2} - (5 c)^{2}$
$= (2 a + 3 b - 5 c) (2 a + 3 b + 5 c)$ .
Now, $\frac{4 a^{2} + 12 a b + 9 b^{2} - 25 c^{2}}{2 a + 3 b + 5 c} = \frac{(2 a + 3 b + 5 c) (2 a + 3 b - 5 c)}{2 a + 3 b + 5 c} = (2 a + 3 b - 5 c)$ .

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