Divide and Simplify:
$4 a^{2} + 12 a b + 9 b^{2} - 25 c^{2}$ by $2 a + 3 b + 5 c$ .

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Solution

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

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Similar questions

4 a^{2} + 12 a b + 9 b^{2} - 25 c^{2}

2 a + 3 b + 5 c

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2 a + 3 b + 5 c

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4 a^{2} - 9 b^{2} - 2 a - 3 b

Factorise:
$4 a^{2} - 9 b^{2} - 2 a - 3 b$

4 a^{2} + 9 b^{2} + c^{2} - 12 a b - 6 b c + 4 a c

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