Here the expression given, [tex] 36x^4-25 [/tex]. We have to factorise the expression.
We know that 36 is a perfect square as [tex] (6)(6) = 36 [/tex], that means [tex] 6^2 = 36 [/tex].
Similarly, [tex] x^4 [/tex] is also a perfect square, as [tex] (x^2)^2 = x^4 [/tex].
25 is also a perfect square, as [tex] 5^2 = 25 [/tex]
So we can write,
[tex] 36x^4 -25 = 6^2(x^2)^2 - 5^2 [/tex]
= [tex] (6x^2)^2-(5)^2 [/tex]
We will use the formula of diffference of two squares now. The formula is,
[tex] a^2-b^2 = (a+b)(a-b) [/tex]
By using this formula we will get [tex] a = 6x^2 , b = 5 [/tex], so we can write,
[tex] (6x^2)^2 - (5)^2 [/tex] = [tex] (6x^2+5)(6x^2-5) [/tex]
We have got the required answer. First option is correct here.
