Question

Find the value by using identity
$1003^{3} + 998^{2} - 102^{3}$
​

Answer 1

Answer:

1003³ + 998² - 102³ = 1008961823

Step-by-step explanation:

Now, 1003³ + 998² - 102³

= (1000 + 3)³ + (1000 - 2)² - (100 + 2)³

= {1000³ + (3 * 1000² * 3) + (3 * 1000 * 3²) + 3³} + {1000² - (2 * 1000 * 2) + 2²} - {100³ + (3 * 100² * 2) + (3 * 100 * 2²) + 2³}

= (1000000000 + 9000000 + 27000 + 27) + (1000000 - 4000 + 4) - (1000000 + 60000 + 1200 + 8)

= 1009027027 + 996004 - 1061208

= 1008961823

Identity rules:

1. (a + b)² = a² + 2ab + b²

2. (a + b)³ = a³ + 3a²b + 3ab² + b³