Question

Evaluate the following products without multiplying directly:
(1) 103 x 107
(ii) 95 x 96
(iii) 104x96​

Answer 1

Answer:

1). 103 × 107 = (100 + 3)(100 + 7)

                    =   (x+a) (x+b) = x² + (a+b)x + ab

                    = (100)² + (3+7)100 + 3 X 7

                    = 10000 + 1000 + 21

                     =11021  

(2) 95 × 96  = (100-5) (100-4) {same identity as above}

                    = (100)² + (-5-4)100 + (-5 X -4)

                    =10000 - 900 + 20

                    =9120

(3) 104 × 96 = (100 + 4)(100 - 4)

                    = (x + a)(x - a) = (x)² - (a)²

                   = (100)² - (4)²  

                   = 10000 - 16

                  = 9984

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