Question

pls solve pls solve this fast it's urgent​

Answer 1

Question :-

Factorize -

$\sf ( 25a^2 + c^2 + 10ac ) - 49 b^2$

Answer :-

Identities used :-

• $\sf (a+b)^2 = a^2 + b^2 + 2ab$
• $\sf a^2 - b^2 = (a + b)(a-b)$

Solution :-

→ $\sf ( 25a^2 + c^2 + 10ac ) - 49 b^2$

→ $\sf [(5a)^2 + (c)^2 + 2 (5a)(c)] - 49b^2$

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By using the identity -

• $\sf (a+b)^2 = a^2 + b^2 + 2ab$

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→ $\sf (5a + c)^2 - 49b^2$

→ $\sf (5a + c)^2 - (7b)^2$

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By using the identity -

• $\sf a^2 - b^2 = (a + b)(a-b)$

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→ $\sf (5a + c + 7b)(5a + c - 7b)$

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$\boxed{\sf ( 25a^2 + c^2 + 10ac ) - 49 b^2 = (5a + c + 7b)(5a + c - 7b)}$