Simplification of Expression by Using Brackets:

Use of brackets allows us to avoid confusion in the problems where we need to carry out more than one number operation.

First, turn everything inside the brackets () into a single number and then do the operation outside which in this case is to multiply by 10.

8 × 100 + 3 × 100 = 100 × (8 + 3) = 100 × 11 = 1100.

Expanding brackets:

i) 102 × 103

= (100 + 2) × (100 + 3) = (100 + 2) × 100 + (100 + 2) × 3

= 100 × 100 + 2 × 100 + 100 × 3 + 2 × 3

= 10,000 + 200 + 300 + 6 = 10,000 + 500 + 6

= 10,506

(ii) 17 × 109

= (10 + 7) × 109 = 10 × 109 + 7 × 109

= 10 × (100 + 9) + 7 × (100 + 9)

= 10 × 100 + 10 × 9 + 7 × 100 + 7 × 9

= 1000 + 90 + 700 + 63 = 1,790 + 63

= 1,853.