If a + b +c = 14, ab + bc + ca = 47 and abc = 15, then the value of $ a^3 + b^3 + c^3 $ is

Step 1: Use the identity

$a^3 + b^3 + c^3 = (a + b + c)^3 - 3(a + b + c)(ab + bc + ca) + 3abc$

Step 2: Substitute the given values

$a^3 + b^3 + c^3 = 14^3 - 3 \cdot 14 \cdot 47 + 3 \cdot 15$

Step 3: Compute each term

$14^3 = 14 \cdot 14 \cdot 14 = 196 \cdot 14 = 2744$

$3 \cdot 14 \cdot 47 = 42 \cdot 47 = 42 \cdot 40 + 42 \cdot 7 = 1680 + 294 = 1974$

$3abc = 3 \cdot 15 = 45$

Step 4: Combine

$a^3 + b^3 + c^3 = 2744 - 1974 + 45 = 770 + 45 = 815$

Answer:

$a^3 + b^3 + c^3 = 815$