Question

Evaluate 998 cube, 99 cube and 104 * 96 using suitable identities

Answer 1

♦(998)³=(1000-2)³
(a-b)³=a³-3ab(a-b)-b³
(1000-2)³=(1000)³-3(1000)(2)-(2)³
=1000000000-6000-8
=999993992

♦(99)³=(100-1)³
(a-b)³=a³-3ab(a-b)-b³
(100-1)³=(100)³-3(100)(1)-(1)³
=1000000-300-1
=1000000-301
=999699

♦(104)(96)
=(100+4)(100-4)
(a+b)(a-b)=a²-b²
(100+4)(100-4)=(100)²-(4)²
=10000-8
=9992

Hope it helps