Question

Evaluate the following product without multiplying directly.


1) 103×107

2) 95×96

Answer 1

Here is the answer to your question!!

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1)  103×107

= (100+103) × (100+17)

= (100)² + (7 + 3) × 100 + 7 × 3

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

= 10000 + 1000 + 21 = 11021

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2 ) 95 × 96

= (90 + 5)(90 + 6)

= (90)² + (5+6)×90 + 5×6

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

= 8100 + 11 × 90 + 30

= 8100 + 990 + 30

= 9120

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Hope it helped!!

Answer 2

Answer:

Step-by-step explanation:

First one 103×107

103=(100+3) and 107=(100+7)

103×107=(100+3)(100+7)

By expanding ,

(100+3)(100+7)

=100×100+3×100+100×7+3×7

=10000+300+700+21

=11021

Second one 95×96

95=(100-5) 96=(100-4)

95×96=(100-5)(100-4)

By expanding

(100-5)(100-4)=

= 100×100-5×100-4×100+5×4

=10000-500-400+20

=9120