Question

LCM of a2+b2 and a4-b4​

Answer 1

Answer:

The LCM is:

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

Step-by-step explanation:

Given polynomials are:

$a^2+b^2\\a^4 - b^4$

We can use factorization to find the LCM of the given polynomials.

Taking the second polynomial, using the identity

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

Applying on 2nd polynomial

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

We can see that $a^2+b^2$ is common in both polynomials, it will be counted only one time. The LCM of given polynomials is:

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