Finding Patterns two digit multiplication part 1

21 * 21

step 1 

20 * 20 =400

step 2

20*1
1*20
-----
40

Step 3

1*1


step 4

441

Base Method

base is 2

21 *21 = 2*(21+1)|(1*1) =44|1=441
21*22 =2*(21+2)|2=462
21*23=2*(24)6 = 486
21*24=2*(25)|4=504

visualise

21*26

considering base 20

21   1(1 away from base 20)

26   6(6 away from base 20)

----------

21+6|1*6

21+6 or 26+1 followed by 1*6

27|6

27*2|6

546


So within 20 or 30 we can do these caluclations easily

Base 30 

33*34

37*3|12

111|12

1122

or 
33*34

I know 35*35=1225

(35-2)*(35-1)

1227-105

1122

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