Question

Find the value of (using algebraic formula):

`((743)^3 − (543)^3)/((743)^2 + (743)(543) + (543)^2)`

Answer 1

Given, `((743)^3 - (543)^3)/((743)^2 + (743)(543) + (543)^2)`

Let 743 = a and 543 = b

Thus, `((743)^3 - (543)^3)/((743)^2 + (743)(543) + (543)^2) = (a^3 - b^3)/(a^2 + ab + b^2)`

⇒ `(a^3 - b^3)/(a^2 + ab + b^2) = ((a - b)(\cancel(a^2 + ab + b^2)))/(\cancel(a^2 + ab + b^2))`

⇒ a – b = 743 – 543

⇒ 200

Hence, the required is 200.