Question

You can easily get this identity by multiplying binomial a - b with itself,
Example 2: Evaluate (42)2 by using Identity-l.
= (40+ 2)2
(42)
Solution:
= 402 + 2 x 40 x 2 + 22
= 1600 + 160 + 4 = 1764
(2m Square of binomial a - b is square of the first term, i.e. a”, plus square of the second
Identity-11 can also be considered as a special case of Identity-1 when 'b' is replaced by - 6
Identity-us.
(a + b)2 = a² + 2ab + b2
Replace 'b' by - b' in the above identity:
(a +(-b))2 = a + 2a x (-6) + (- 6)2
(iii)
(a - b)2 = a? - 2ab + b2 which is identity-II.
(vi)
term, t.e. 6. minus twice the product of the two terms, i.e. 2ab.
You can verify the above result by taking any values of a and b. Say, a = 5, 6 = 3 then,
L.H.S. = (a - b)2 = (5 - 3)2 = 22 = 4
R.H.S. = a2 - 2ab +62
Worksheet 1
uslo
(8x + 3y)2
Thus,
1.
Find the following by using Identity-I.
(2x+52
(0.2x + 1.5y)2
(0)
(V)
(iv) (7pq + 4ab)
(iii) (8.17
(vi) (10.22
2. Evaluate the following by using Identity-I.
(101)
(ii) (52)
(iv) (203)
(V) (410)
= 52 - 2x 5 x 3 + 32 = 25 - 30 + 9 = 4
L.H.S. = R.H.S.
hus, Identity-II is verified.
Identity-11
(a - b)2 = a2 - 2ab +62
bu can verify the above result geometrically by the following activity:
ctivity 2
(a - b)2 = (a - b)(a - b)
ep 1 : Take a square ABCD with side 5 cm.
ala - b)-b(a - b)
ep 2
: Draw a square AEFG with side 3 cm on it. Its area is 32 cm? or (5 - 2)2 cm?.
= a? - ab- ba + 62
А 4
3
E
► 2-B
A
A 3 & 2 B
= a2 - 2ab + b2
3
5
Similarly, (6 - a) can also be found.
G
F
F
H
(6 - a)2 = 62 - 2ba + a2
= 02 - 2ab +62
D
(6 - a)2 = (a - b)2
110
Thus,
(1)
111​

Answer 1

Answer:

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