1. The document discusses algebraic identities for expressions of the form (a + b)2, (a - b)2, and (a + b)(a - b). It derives the identities (a + b)2 = a2 + 2ab + b2, (a - b)2 = a2 - 2ab + b2, and (a + b)(a - b) = a2 - b2. 2. Examples are provided to demonstrate expanding expressions and simplifying them using the derived identities. Specific examples include finding the value of (17)2, (20 - 3)2, and (17 × 23). 3. Practice problems are given involving expanding expressions

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16. 4 2
X 0 = X2
a+b=
( a + b)2

17. –1
a2 + ab + ab +b2 = a2 + 2ab + b2
(a + b)2 = a2 + 2ab + b2

18. ,
:-
(a + b)2 = a2 + 2ab + b2
:-
(17)2 = (10 + 7 )2
= 102 + 2(10) (7) + 72
= 100 + 140 + 49
= 289

19. -2
(a – b)2 + ab + (a – b)b = (a – b)2 + ab + ab – b2
a2 = (a – b)2 +2 ab – b2
=> (a - b)2 = a2 - 2ab + b2

20. ,
:-
(a - b)2 = a2 - 2ab + b2
:
(17)2 = (20 - 3 )2
= 202 - 2(20) (3) + 32
= 400 - 120 + 9
= 289

21. -3 a(a-b)+b(a-b)
= > a2-ab+ba-b2
(a + b) (a –b) = a2 – b2

22. ,
:-
(a + b) (a –b) = a2 – b2
: (17 X 23) = (20 - 3) (20 +3)
= 202 - 32
= 400 – 9
= 391

23. ?
,
(a +1)(a+2) = a2 + 3a +2
a=2
(2+1)(2+2)=22 + 3(2)+2
12=12
a = -3 , L.H.S = R.H.S |
(-3+1)(-3+2)=(-3)2+3(-3)+2
2=2

24. 8. |
1.
2. -
(a + b)2 = a2 + 2ab + b2 -------------------------(1)
(a - b)2 = a2 - 2ab + b2 -------------------------(11)
(a + b) (a –b) = a2 – b2 --------------------- (111)

25. 9.
1 (1)
(i) (2x + 3y)2
(ii) 1032
2 (11)
(i) (4p - 3q)2
(ii) (4.9)2
3 (111)
(i) (3/2 m + 2/3 n) (3/2 m – 2/3 n)
(ii) 9832 - 172
(iii) 194 X 206

26. 10.
1. . (a + b)2 = a2 + 2ab + b2, a
=3 and b = 4
I
2.
(104)2.
3. .
104 X 96

27. 