Question

evalulate the following products with out actual multiplication
1) 101*99 2) 999*999
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Answer 1

Answer:

1. 999*999

=(1000-1)*(1000-1)=(1000-1)∧2

=(1000)∧2+1∧2-2*1000*1

=1000000+1-2000

=998001

2. 30.5*29.5

=(30+ 0.5)*(30-0.5)

=(30)∧2-(0.5)∧2

=900-0.25

=899.75

3. (50*1/2)*(49*1/2)

=(50*49)*1/4

=(50*(50-1)*1/4

=(2500-50)*1/4

=2450/4

=1225

Hope this is helpful!

Answer 2

1) (100+1)(100-1)
(100)square + [1+(-1)]100+(1*-1)
10000+(1-1)100+(-1)
10000+0-1
10000-1
9999
2) I don’t know