This document describes how to use cut-out shapes to verify several algebraic identities through visual representation and calculation of areas. It provides instructions and materials for verifying the identities (a+b)2, (a-b)2, and a2 - b2 = (a+b)(a-b) using squares, rectangles, and other shapes cut out of paper or cardstock. Tables are included to record the values being tested and calculate both sides of each identity to check for equality. The goal is to visually and physically demonstrate several fundamental algebraic relationships using a hands-on math kit.

1. ALGEBRIC IDENTITIES
NCERTSECONDARY MATHSKITS

2. Cut outs for
algebraic identities
Maths kit
Material supplied

3. ALGEBRIC IDENTITIES
OBJECTIVE
To verify the algebraic identities
(i) (a+b)2
= 𝑎2
+2ab + 𝑏2
(ii) (a−b)2
= 𝑎2
−2ab + 𝑏2

4. MATERIAL REQUIRED
𝒂𝟐
𝒃𝟐
ab
ab Cut out of square a
Cut out of square b
Cut out of rectangle ab
Cut out of rectangle ab

5. MATERIAL REQUIRED
𝒂𝟐
𝒃𝟐
ab
ab
Arrange the four cut outs on table as
shown
It is a square of side (a+b) Units.
Find the area of formed figure= Side X Side
(a+b)(a+b)= (𝒂 + 𝒃)2
(𝒂 + 𝒃)𝟐
= 𝒂𝟐
+2ab+ 𝒃𝟐
Also find the area of individual figures
𝒂2+2ab+ 𝒃2

6. - - - - - - - - -
- - - - - - - - -
4 25
24
12 25 5
9
9 16 12
6
49 7 49
TABLE 1
S.No
.
a b 𝒂2
𝒃2 ab 2ab 𝒂2+2ab+𝒃2 (a+b) (𝒂 + 𝒃)2
1
2
3
4
2
3 4
3

7. (a−b) 𝟐
=𝒂𝟐 − 𝟐𝐚𝐛 + 𝒃𝟐
𝒂𝟐
𝒃𝟐
ab
ab
Put cut outs on a table as shown.
Side of green colour cut out is a units.
Side of blue colour cut out is b units.
Sides of red colour cut out is a Xb
units.
Area of uncovered portion is
(𝒂 − 𝒃)2
= 𝒂2
+ 𝒃2
-2ab.
(𝒂 − 𝒃)𝟐
= 𝒂𝟐
+ 𝒃𝟐
-2ab.

8. - - - - - - - - -
- - - - - - - - -
25 4
56
30 4 2
9
49 16 28
15
9 3 9
TABLE 2
S.No
.
a b 𝒂2
𝒃2 ab 2ab 𝒂2 −2ab+𝒃2 (a-b) (𝒂 − 𝒃)2
1
2
3
4
5
7 4
3

9. ab
𝑏2
𝑎2
Extension
Varifying the identity (𝑎 + 𝑏)2
-4ab= (𝑎 − 𝑏)2
ab
ab
ab
ab
ab

10. ALGEBRIC IDENTITIES
OBJECTIVE
To verify the algebraic identities
𝐚𝟐
− 𝐛𝟐
=(a + b)(a-b)

11. 𝒃𝟐
Cut out of square a
Cut out of square b
Cut out of trepizium ab
Cut out of trepizium ab
𝒂𝟐
- 𝒃𝟐
=(a+b)(a-b)
𝒂𝟐

12. 𝒂𝟐
𝒂𝟐
- 𝒃𝟐
=(a+b)(a-b)
(a-b)
(a+b)
𝒃𝟐

13. 𝒂𝟐
- 𝒃𝟐
=(a+b)(a-b)
𝒂𝟐
Put cut outs on a table as shown.
Side of yellow colour cut out is a units.
Side of green colour cut out is b units.
Sides of brown colour cut out is a ,b
units.
Area of brown portion is (a+b)(a-b)
(a+b)(a-b)= 𝒂𝟐
- 𝒃𝟐
.
𝒃𝟐
(a+b)(a-b)
Area of yellow portion under brown
portion is 𝒂2
- 𝒃2
.

14. - - - - - - - - -
- - - - - - - - -
25 Yes
3
2 16 16
9
49 16 11
8
33 33 Yes
TABLE 3
S.No
.
a b 𝒂2
𝒃2 a+b a-b 𝒂2 − 𝒃2 (a+b)(a-b)
1
2
3
4
5
7 4
3
Is 𝒂2
− 𝒃2
=(a+b)(a-b)

15. Geogebra files

16. Thank you