Have you ever wondered why is (a-b)^2 = a^2 - 2ab + b^2? Here is a presentation that will explain this algebraic identity. This was one of the algebraic identities that ancient Indian mathematician Bhaskaracharya-II (1114-1193 CE) gave in his mathematical treatise 'Lilavati' (1150 CE)

1. Squaring – 2
(from Bhaskara’s Lilavati)
Vinay Nair
SCHOOL OF VEDIC MATHS

2. • (a - b)2 = a2 - 2ab + b2

3. Geometric Representation
(i) 82

4. (i) 82
(10 - 2)2

5. (i) 82
(10 - 2)2

6. (i) 82
(10 - 2)2

7. 102
- 10 x 2
- 10 x 2
+
22
= 100
= 20
= 20
= 4
64
100 – 2 x 20 + 4 = 64

8. More examples
(ii) 292
(30 - 1)2
302
= 900
- 2 x 30 x 1 = -60
840
+
12 = 1
841

9. More examples
(iii) 472
(50 - 3)2
502
= 2500
- 2 x 50 x 3 = -300
2200
+
32 =
9
2209

10. More examples
(iv) 1922
(200 - 8)2
2002
- 2 x 200 x 8
+
82
= 40000
= -3200
36800
=
64
36864

11. More examples
(v) 2472
(250 - 3)2
2502
- 2 x 250 x 3
+
32
= 62500
= -1500
61000
=
9
61009

12. Thank you!