how do you factorise 16 - x^4 ?

16 - x^4
= (4)^2 - (x^2)^2
= (4 - x^2)(4 + x^2) Using the Difference Of Perfect Squares rule
If you'd like to factorise further,
= (2 - x) (2 + x) (x^2 + 4)

x^4=(2)^4
hence x=2!!!
i.e luk for a value whose ^4 is equal to 16 which in this case is 2!!!!

16 - x^4
= (4 + x^2)(4 - x^2)
= (4 + x^2)(2 + x)(2 - x)

(4 - x²) (4 + x²)
(2 - x) (2 + x) (4 + x²)

(a+b)(a-b) = a^2 - b^2

so a^2 = 16 and b^2 = x^4

= 16 - x^4
= (4 + x^2)(4 - x^2)

since, if a^2 = x^4, then a = x^2

(4-x^2)(4+x^2)
(2-x)(2+x)(4+x^2)

follows the rule of difference of squares

a^2-b^2=(a-b)(a+b)

16 - x^4 = 2^4 - x^4 = (2^2+x^2)(2^2-x^2) = (4+x^2)(2+x)(2-x)