The LCM of$$(a^3+b^3 )$$​ and $$(a^4-b^4 )$$​ is:

Correct option is D

Formula Used:

​$$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$​​

​$$a^4 - b^4 = (a - b)(a + b)(a^2 + b^2)$$​​

Solution:

​$$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$​​

​$$a^4 - b^4 = (a - b)(a + b)(a^2 + b^2)$$​​

The LCM will include all the distinct factors that appear in both expressions:

LCM = $$(a - b)(a + b)(a^2 - ab + b^2)(a^2 + b^2)$$ =$$(a^3+b^3 )(a^2+b^2 )(a-b)$$​​