Simplify the following expression.

$\frac{(777×777×777)+(423×423×423)}{(777×777)-(777×423)+(432×423)} × \frac{1}{(77-47)}$

40

$\frac{(777×777×777)+(423×423×423)}{(777×777)-(777×423)+(432×423)} × \frac{1}{(77-47)}$ = ?

= a³ + b³ = ( a + b ) ( a² + b² - ab )

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

If we compare $\frac{(777×777×777)+(423×423×423)}{(777×777)-(777×423)+(432×423)}$ with the eqation given above.

Then the value of a = 777 and b = 423

and the value of a + b = 777 + 423 = 1200 put this value in required equation.

So, $\frac{(777×777×777)+(423×423×423)}{(777×777)-(777×423)+(432×423)} × \frac{1}{(77-47)}$ = $1200 × \frac{1}{(77-47)}$

= $1200 × \frac{1}{(30)}$ = 40