Question

Factorise 36a^4 - 97a^2b^2 +36b^4

Answer 1

$\huge\boxed{\mathcal{\fcolorbox{red}{blue}{Hope \:This \:Helps\:u}}}$

Answer 2

$36a^4 - 97a^2b^2 +36b^4=(2a+3b)(2a-3b)(3a+2b)(3a-2b)$

Step-by-step explanation:

Given : Expression $36a^4 - 97a^2b^2 +36b^4$

To find : Factories the expression ?

Solution :

Expression $36a^4 - 97a^2b^2 +36b^4$

Applying middle term split,

$36a^4 - 16a^2b^2-81a^2b^2+36b^4$

$4a^2(9a^2-4b^2)-9b^2(9a^2-4b^2)$

$(4a^2-9b^2)(9a^2-4b^2)$

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

Apply identity, $a^2-b^2=(a+b)(a-b)$

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

The factorization form is

$36a^4 - 97a^2b^2 +36b^4=(2a+3b)(2a-3b)(3a+2b)(3a-2b)$

#Learn more

Factorise  36a^2 +36a + 9

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