1. Algebraic Expressions
and
Identities

2. Identities to be remembered:
(a + b)2 = a2 + b2 +2ab
(a - b)2 = a2 + b2 - 2ab
(x + a)(x + b) = x2 + (a + b)x + ab
(a - b)(a + b) = a2 – b2
(a+b)3 = a3 +b3 + 3ab(a+b)
=a3 + 3a2b+3ab2 + b3
(a-b)3 = a3 - b3 - 3ab(a - b)
=a3 - 3a2b +3ab2 - b3

3. The value of :
(67.542) (32.458)2
100
Choose the correct option:
b)10
a) 1
d)20
c)100

4. Find the missing term in the following equation:?
(2x+ 3) (2x+ 4) = 4x
Choose the correct option:
a) 7x
b) 14x
14x
Ans:
c) 6x
d) 8x

5. Fill in with he missing term:
(-15x)
(5x + 4)(5x – 7) = 25x
= 25x x
Choose the correct option:
a) 15x
b) 55x
c) -3x
d) -15x

6. Fill in with the missing term:
27a
(-3a - 7)(-3a – 2) = 9a
Choose the correct option:
a) 27a
c) -27a
b) 15a
d) -15a

7. Fill in with the missing term:
(-8a)
(-2a + 8)(-2a – 4) = 4a
= 4a
- 8a
Choose the correct option:
a) -8a
c) 8a
b) 4a
d) 16a

8. Fill in with the missing term:
70pq
(5p + 7q)2 = 25p q2
(-2a + 5b)2 = 4a b2
= 4a b2
( -3f - 8g)2 = 9f g2
(-20ab) ab
48fg

9. Find the missing term in the following equation:?
Choose the correct option:
a) 2xy
b) -2xy
a) 2xy
ANS:
c) 12xy
d) -12xy

10. = + + ab (-xy) - xy Fill in with the missing term: a) ab b) = += ab
(-xy)
- xy

11. (-pq) - pq Fill in with the missing term: = +=
(-pq)
- pq

12. If 6x – 4y = 3 , xy = 2 , then :
36x2 + 16y2 =
105

13. If (-15p – 4q) = -3 , pq = -1, then :
225p2 + 16q2 =
129

14. If (3a + 5b) = - 4 , 9a2 + 25b2 = -14 , then :
ab=
01(one)

15. If 9m2 + 49n2 = -3 , mn = 2 , then:
3m + 7n = 09

16. If 25a2 + 81b2 = 216 , ab = -4 ,
then:
5a – 9b = 24

17. If 4a b2 = 48 , ab = -2 ,
then:
a – 6b = 06

18. If 25x y2 = -90 , and 5x + 8y =10 , then :
5x – 8y = -9

19. 02 If 256x2 - 81y2 = 72, 16x - 9y = 12p and 16x + 9y = 3q , then :
pq = 02

20. If , then : 79

21. If , then : 38

22. If , then : 12

23. If , then : 20

24. If , then : 15

25. If , then : 23

26. Expand : (3a + 2b)3 = (4x + 7y)3 = ................ 27a3 + 54a2b

27. Expand : (8y – 5x )3 = (3b – 7a)3 = 512y3 - 960y2x + 600x2y - 125x3
512y3
y2x
+ 600x2y x3
27b3
b2a
ba2 a3

28. Expand : (-2d + 7a)3 = (-a - 6c)3 = - 8d3 + 84d2a - 294da2 + 343a3
- a3
- 18a2c
- 108ac2
- 216c3