Answer:
The LCM is:
[tex](a^2+b^2)(a+b)(a-b)[/tex]
Step-by-step explanation:
Given polynomials are:
[tex]a^2+b^2\\a^4 - b^4[/tex]
We can use factorization to find the LCM of the given polynomials.
Taking the second polynomial, using the identity
[tex]a^2 - b^2 = (a+b)(a-b)[/tex]
Applying on 2nd polynomial
[tex](a^2)^2-(b^2)^2\\=(a^2+b^2)(a^2-b^2)\\=(a^2+b^2)(a+b)(a-b)[/tex]
We can see that [tex]a^2+b^2[/tex] is common in both polynomials, it will be counted only one time. The LCM of given polynomials is:
[tex](a^2+b^2)(a+b)(a-b)[/tex]
