Find the value of (?) in the following.

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

Correct option is C

Given:

​$$(a^2 - b^2) : (a^2 - ab) :: (a^3 + b^3) : \ ?$$​​

Formula Used:

​$$a^2 - b^2 = (a - b)(a + b)$$​​

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

Solution:

$$\frac{a^2 - b^2}{(a^2 - ab)} = \frac{(a^3 + b^3)}{?}$$​

​$$? = \frac{(a^2 - ab)(a^3 + b^3)}{a^2 - b^2} = \frac{(a^2 - ab)(a + b)(a^2 - ab + b^2)}{(a - b)(a + b)}$$​​

​$$= \frac{a(a - b)(a^2 - ab + b^2)}{a - b} = a(a^2 - ab + b^2)$$​​