SRR. SRR. WELCOME TO THE WORLD OF SRR CLASSES. Ganita Gatha-(a+b)2. 

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VISUALISING IDENTITIES SRR ( +b)2 — cz2 + 2ab + CLASSES Shaping Minds. Building Future THE SQUARE OF (a+b) IDENTITY: An algebraic identity is true for all values Of the variables-. 

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VISUALISING IDENTITIES
SRR
( +b)2 — cz2 + 2ab +
CLASSES
Shaping Minds. Building Future
THE SQUARE OF (a+b)
IDENTITY:
An algebraic identity is true
for all values Of the variables-

REMEMBER:
= a2 +
Square of
a
2ab + b2
Twice the Square of
product
b
of a and b

SRR CLASSES Shaping Minds, Building Future -NÖC VISUALISING IDENTITIES THE SQUARE OF (a+b) IDENTITY: b2 An algebraic identity is true for all values of the variables_. 

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SRR
CLASSES
Shaping Minds, Building Future
-NÖC
VISUALISING IDENTITIES
THE SQUARE OF (a+b)
IDENTITY:
b2
An algebraic identity is true
for all values of the variables_

1. VISUAL REPRESENTATION
Consider a square with side (a + b)
a+b
ab
ab
Add all the areas:
Top-left square
has area a
Top-right rectangle
has area ab
Bottom-left rectangle
has area ab
Bottom-right square
has area b2

2. ALGEBRAIC VERIFICATION
— a2 + 2ab + b2

3. EXAMPLE
Let a = 3, b = 2
(3 + 2) 52
2 = = 25
a2 + 2ab + b2 =
32 + + 22
12+4
= 25

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SRR. SRR. WELCOME TO THE WORLD OF SRR CLASSES. Ganita Gatha-(a-b)2. 

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SRR CLASSES Shaping Minds, Building Future VISUALISING IDENTITIES THE SQUARE OF (a -b) IDENTITY: = — 2ab + An algebraic identity is true for all values of the variables.. 

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SRR
CLASSES
Shaping Minds, Building Future
VISUALISING IDENTITIES
THE SQUARE OF (a -b)
IDENTITY:
= — 2ab +
An algebraic identity is true
for all values of the variables.

REMEMBER:
2
a
Square of
— 2ab
Twice the
product
of a and b
Square of

SRR CLASSES Shaping Minds. Building Future VISUALISING IDENTITIES THE SQUARE OF (a —b) IDENTITY: cm2 — 2ab + An algebraic identity is true for all values Of the variables.. 

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SRR
CLASSES
Shaping Minds. Building Future
VISUALISING IDENTITIES
THE SQUARE OF (a —b)
IDENTITY:
cm2 — 2ab +
An algebraic identity is true
for all values Of the variables.

2. ALGEBRAIC VERIFICATION
a(a — b) — b(a — b)
a2 — ab
— a2 — ab
2
— b(a — b)
— (ba — b2)
— ba + b2
— ab
a2 - 2ab

3. EXAMPLE
Let a = 8, b = 5
(8 - = 32 = 9
a2 — 2ab + b2
= 82 -
+ 52
= 64 - 80 + 25 =

1. VISUAL REPRESENTATION
Consider a square with side a.
Remove a strip Of width b from the right side
and a strip of width b from the bottom side.
o
b
ab
b(a-b)
Area Of remaining part (shaded region):
— ab — b(a — b) = a2
— ab
= a2 — 2ab + b2
Top-left square
has area (a —
Right rectangle
has area ab
Bottom rectangle
has area — b)
Removed bottom-right
square has area b2
— ba + b2

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SRR. SRR. WELCOME TO THE WORLD OF SRR CLASSES. Ganita Gatha-(a+b+c)2. 

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VISUALISING IDENTITIES SRR CLASSES Shaping Minds. Building Future IDENTITY: 2 An algebraic identity is true THE SQUARE OF (a + b + c) for all values of the variables.. 

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VISUALISING IDENTITIES
SRR
CLASSES
Shaping Minds. Building Future
IDENTITY:
2
An algebraic identity is true
THE SQUARE OF (a + b + c)
for all values of the variables.

Area of the whole square = Sum of all parts
a2 + '02 + c2 + 2ab + 2bC + 2ca

REMEMBER:
(a b c) 2 = a 2 + b 2 + c 2 + + 2bC +
Square Square Square Twice the
of C product
of a
of b
of a and b
Twice the
product
of b and c
Twice the
product
of c and a

SRR Shaping Future VISUALISING IDENTITIES THE SQUARE OF (a + b + c) IDENTITY: 2 An algebraic identity is true for Of the variables_. 

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1. GEOMETRICAL REPRESENTATION
Consider a square with side (a + b + c).
a
b
c
2
a
ab
ac
ab
bc
ac
bc
2
LEGEND
Top-left square
Area = a
Center square
Area = b2
Bottom-right square
Area = c2
Rectangles with sides
a and b (two of them)
Total area = 2ab
Rectangles with sides
b and c (two of them)
Total area = 2bc
Rectangles with sides
a and c (two of them)
Total area = 2ca

SRR
Shaping Future
VISUALISING IDENTITIES
THE SQUARE OF (a + b + c)
IDENTITY:
2
An algebraic identity is true
for Of the variables_

Area of the whole square = Sum of all parts
(a + b + c) 2 = a 2 + + c2 + 2ab + 2bC + 2ca

2. ALGEBRAIC VERIFICATION
2ab + 2bc + 2ca
a2 + + c2 + 2ab + 2bC + 2ca

3. EXAMPLE
Let a = 2, b
2 92 _
— 81
2
a
- 22 + 32 + 42 + + +
4 + + 16 12 -+- 24 16 =
81

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SRR. SRR. WELCOME TO THE WORLD OF SRR CLASSES. Ganita Gatha-(a)2. 

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SRR CLASSES Shaping Minds, Building Future VISUALISING IDENTITIES LET'S UNDERSTAND WITH A PICTURE! IDENTITY: A beautiful connection between areas and algebra!. 

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SRR
CLASSES
Shaping Minds, Building Future
VISUALISING IDENTITIES
LET'S UNDERSTAND WITH A PICTURE!
IDENTITY:
A beautiful connection
between areas and algebra!

The whole square (of side a) is equal to the sum of
the green rectangle and the small square b2.

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1. GEOMETRICAL REPRESENTATION
Consider a square of side a.
(a + b)(a — b)
a
b2
Green part:
Area = (a + b)(a — b)
Right strip:
Area = ab
Bottom strip:
Area = ab
Bottom-right square:
Area = b2
The whole square (of side a) is equal to the sum of
the green rectangle and the small square 1)2.

2. FROM THE FIGURE TO THE IDENTITY
2
Area of whole square of side a = a
Area —
(Green rectangle)
(Small square)
2
a

3. NUMERICAL EXAMPLE
Let a = 55 and b = 5
2
= (a + b)(a — b) + b2
a
= (55 + - 5) + 52
60 x 50 + 25
3000 + 25
3025

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SRR CLASSES Shaping Minds, Building Future VISUALISING IDENTITIES + 3a2b + 3ab2 + b3 LET'S UNDERSTAND WITH CUBES! IDENTITY: (a+b) a3 + 3a2b + 3ab2 + b3 A beautiful connection between volume and algebra!. 

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SRR
CLASSES
Shaping Minds, Building Future
VISUALISING IDENTITIES
+ 3a2b + 3ab2 + b3
LET'S UNDERSTAND WITH CUBES!
IDENTITY:
(a+b) a3 + 3a2b + 3ab2 + b3
A beautiful connection
between volume and algebra!

Think in 3D,
Understand in
Depth!
SRR
cuasses

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'5. NUMERICAL EXAMPLE*
a3 + 3a2b + 3ab2 + b3
RHS:
Let a = 2 and
- 23
LHS: (a + b)3
= (2 + = 53 = 125
= 8 + 36 + 54 + 27 = 125
33
LHS = RHS = 125
Identity Verified!

b 3. ADDING THE VOLUMES
Add the volumes of all 8 parts.
= a3 + 3a2b + 3ab2 + b3
Therefore,
(a+b)3 =
a3 + 3a2b + 3ab2 + b3

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