If a + b + c = 9 and ab + bc + ca = 18, then the value of $$a^3 + b^3 + c^3 - 3abc$$ is:

Given that in the question, a+b+c = 9 and ab +bc +ca = 18 

then the value $$a^3 + b^3 -3abc $$ = ?(sove that given expression)

$$a^3+b^3 - 3abc $$

$$\Rightarrow (a+b+c) (a^2 +b^2 +c^2 -ab -bc -ca)$$

$$\Rightarrow 9 (a^2 +b^2 +c^2 - 18) $$

$$\Rightarrow 9 [ (a+b+c)^2 -2(ab+bc+ca) - 18 ] $$

$$\Rightarrow 9[ (9)^2 -2(ab+bc+ca) -18 ]$$

$$\Rightarrow 9 [ 81 - 2\times18 - 18 ] $$

$$\Rightarrow 9[81 -36 -18]$$

$$\Rightarrow 9[81 -54]$$

$$\Rightarrow 9 \times 27 $$

$$\Rightarrow 243 Ans $$