Question

EVALUATE THE FOLLOWING WITH USING SUITABLE IDENTITIES

1. (998)³​

Answer 1

${(998)}^{3} \\ = {(1000 - 2}^{3} \\ using \: identity \: {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) \\ {(1000)}^{3} - {2}^{3} - 3 \times 1000 \times 2(1000 - 2) \\ 1000000000 - 8 - 6000 \times 998 \\ = 1000000000 - 8 - 5988000 \\ = 999999992 - 5988000 \\ = 994011992$