Question

evaluate the following products without multiplying directly
1)105×106
2)103×107
3)207×193
4)103×97​

Answer 1

1}11130

2}11021

3}39951

4}9991

Answer 2

$105 \times 106 \\ \\ = (105.5 - 0.5)(105.5 + 0.5) \\ \\ = {(105.5)}^{2} - {(0.5)}^{2} \\ \\ = 11130.25 - 0.25 \\ \\ = 11130 \\ \\ \\ 103 \times 107 \\ \\ (105 - 2)(105 + 2) \\ \\ {105}^{2} - {2}^{2} \\ \\ = 11025 - 4 \\ \\ = 11021 \\ \\ \\ 207 \times 193 \\ \\ = (200 + 7)(200 - 7) \\ \\ = {200}^{2} - {7}^{2} \\ \\ = 40000 - 49 \\ \\ = 39951$

$103 \times 97 \\ \\ (100 + 3)(100 - 3) \\ \\ = {100}^{2} - {3}^{2} \\ \\ = 10000 - 9 \\ \\ = 9991$

hope it helps