Slide 1

Algebraic
Expressions
and

Identities


Slide 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


Slide 3

The value of :
(67.542)2 -

(32.458)2

75.458 - 40.374

100
..........................

Choose the correct option:
a) 1

c)100

b)10

d)20


Slide 4

Find the missing term in the following
equation:

?
(2x+ 3) (2x+ 4) = 4x2 + ...........
+ 12
Choose the correct option:
a) 7x

b) 14x

c) 6x

d) 8x

14x
Ans:.................


Slide 5

Fill in with he missing term:

(-15x) - 28
(5x + 4)(5x – 7) = 25x2 + ................
- 15x - 28
= 25x2 ................
Choose the correct option:
a) 15x

b) 55x

c) -3x

d) -15x


Slide 6

Fill in with the missing term:
27a
(-3a - 7)(-3a – 2) = 9a2 + ................+
14

Choose the correct option:
a) 27a

c) -27a

b) 15a

d) -15a


Slide 7

Fill in with the missing term:
(-8a)
(-2a + 8)(-2a – 4) = 4a2 + ................32
- 8a = 4a2 ............
Choose the correct option:
a) -8a

c) 8a

b) 4a

d) 16a

32


Slide 8

Fill in with the missing term:

(5p + 7q)2 = 25p2 + 70pq
..........

+ 49q2

(-20ab) + 25b2
(-2a + 5b)2 = 4a2 + ...........
- 20ab + 25b2
= 4a2 .................
48fg
( -3f - 8g)2 = 9f2 + .............
+64g2


Slide 9

Find the missing term in the following
equation:

(

3x



4

4y
3

2

)



9x

2



16 y

16

2

?

 ........

9

Choose the correct option:
a) 2xy

b) -2xy

c) 12xy

d) -12xy

a) 2xy
ANS: ............................


Slide 10

Fill in with the missing term:

6a

7b

2

2

6a

(

(
)

)
a)
7
7
12
36

(

(

3x
4y



2 y
3x

49

2

2

)

)
2

b

144
2



ab
 ..........

12

= 49 a +
b)

7b

2

9x
..............
16 y
9x

2

2

4y

(-xy)

+ .............. + ...........

2

= ...............
+
2
16 y

+ ab
2

9x
4y

2

xy
............ -..........
9x

2


Slide 11

Fill in with the missing term:

(

8p
5q



5q
16 p

2

)



16 p

2

25 q

2

(-pq)

.................
+ .................
+ .............
2
2

25 q
16 p

256 p

2

25 q

2

pq
= ................
+ ................. - ................
2
256 p
25 q
2


Slide 12

If

6x – 4y = 3 , xy = 2 , then :

105
36x2 + 16y2 = .................


Slide 13

If (-15p – 4q) = -3 ,
then :

pq = -1,

129
225p2 + 16q2 = .................


Slide 14

If (3a + 5b) = - 4 ,
then :

01(one)
ab= ..................

9a2 + 25b2 = -14 ,


Slide 15

If 9m2 + 49n2 = -3 ,
then:

09
3m + 7n = ...............

mn = 2 ,


Slide 16

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

ab = -4 ,


Slide 17

If 4a2 + 144b2 = 48 ,
then:
06
a – 6b = ...............

ab = -2 ,


Slide 18

If 25x2 - 64y2 = -90 , and 5x + 8y =10 ,
then :
-9
5x – 8y = ........................................


Slide 19

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

02
pq =................


Slide 20

If

x 

1

 9,

then :

x

x

2



1

x

2

79
 ...................


Slide 21

1

If x 

 6,

x

x

2



1

x

2



38

................

then :


Slide 22

If x

2



x 

1

x

2

1
x

 142,

then :

12
................................


Slide 23

If x

2



x 

1

x

2

 398

1
x

, then :

20
.............


Slide 24

If x

2



x 

1

x

2

 227

1
x

, then :

15
 .......................


Slide 25

If x

2



x 

1

x

2

 531

1
x



, then :

23

......................


Slide 26

Expand :
27a3 +
(3a + 2b)3 =................

(4x +

7y)3

................
54a2b + ................
36ab2 + ................
8b3

3 + 336x2y
2 + 343y3
64x
+
588xy
= .............. ................ ............. ..........


Slide 27

Expand :
(8y – 5x )3 =

..............
512y3 -.................
960y2x ..............
+ 600x2y - ..............
125x3

(3b – 7a)3 =

27b3 -................
189b2a ................
+ 441ba2..............
- 343a3
................


Slide 28

Expand :
(-2d + 7a)3 =

(-a -

6c)3

=

- 8d3 +.............
84d2a .............
- 294da2
.............

+
343a3
.............

-.............
a3
- .............
18a2c -.............
108ac2 - .............
216c3