3. Multiplication
Substruction
for
Quadratic
Form
Black Hole

4. Multiplication
x

5. MULTIPLICATION
7
8 15697 35 x
4
6
26 4 0 4 0
3 2
6 0 6 0 8
5 7 5 1
8 2
9
2
6
8 4
2 3 2 22 10
54
3
4
346
354 3
0 3 2
0 3 1

6. Next step
7
8 15697 35 x
4
6
26 4 0 4 0
3 2
6 0 6 0 8
5 7 5 1
8 2
9
2
6
8 4
2 3 2 22 10
54
3
4
346
354 3
0 3 2
0 3 1
11212222
822 8
5
8 7 4 1
4
7

7. Finally
78965153 × 476 =
47587412828
BACK

8. Substruction for
Quadratic Form
21522 – 1322 = ?

9. 21522 – 1322 =
2152 + 132 = 2284

10. 21522 – 1322 =
2152 132 = 2020

11. 21522 – 1322 =
2152+132 = 2284
21522 – 1322 =
2152-132 = 2020

12. 0
22 48 x
2
2
84 4 6
4 4 6 8
0 0 0 0
10 00
0
0
0 0 0
0 1 0
00 0 0 0
0 0 0 0
1 1
03 6 8
1
6
4
0

13. Finally
21522 – 1322 =
4613680
BACK

14. Is it true that 1 = 1?
X2 = X2
X2 - X2 = X2 - X2
X (X - X ) = ( X + X )( X - X )
X (X - X ) = ( X + X )( X - X )
X = X + X
X = 2 X
1 = 2 (1)
So …….
1 = 2
+( -X2 )
X2 - Y2 = (X - Y )(X + Y)