Question

16a^4 - 81b^4 factorize in detail

Answer 1

Here is your answer hope it helps

Answer 2

Solution:

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Given :

To factorize :

$16a^4 - 81b^4$

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⇒ $16a^4 - 81b^4$


As, we know that,

a² - b² = (a + b)(a - b)

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⇒ $(4a^2)^2 - (9b^2)^2$

⇒ $(4a^2 - 9b^2)(4a^2 + 9b^2)$

⇒ $((2a)^2 - (3b)^2)((2a)^2 + (3b)^2)$

As we know that,

a² + b² = (a + b)² - 2ab

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⇒ $(2a + 3b)(2a - 3b)((2a^2 + 3b^2)$

⇒ $(2a + 3b)(2a - 3b)((2a + 3b)^2 - 2(2a)(3b))$

⇒ $(2a + 3b)(2a - 3b)((2a + 3b)^2 - 12ab))$


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                            Hope it Helps !!

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