Factor completly x481y4 Is or is not primeSolutionx481y4 x2

Factor completly

x⁴-81y⁴

Is or is not prime.

Solution

x4-81y4

= (x^2)^2 -(9y^2)^2

Using the formula : a^2 - b^2 = (a+b)(a-b)

we get = (x^2)^2 -(9y^2)^2

= (x^2 - 9y^2)(x^2 +9y^2 )

again for x^2 -9y^2 = x^2 -(3y)^2 = (x+3y)(x-3y)

= (x^2 - 9y^2)(x^2 +9y^2 )

=(x+3y)(x-3y)(x^2 +9y^2)