algebraic expressions and identities. identities to be remembered: (a + b) 2 = a 2 + b 2 +2ab (a -...
TRANSCRIPT
Algebraic Expressions
and
Identities
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
The value of :
(67.542)2 - (32.458)2
75.458 - 40.374
a) 1 b)10
c)100d)20
Choose the correct option:
100..........................
Find the missing term in the following equation:
(2x+ 3) (2x+ 4) = 4x2 + ........... + 12?
a) 7x b) 14x
c) 6x d) 8x
Ans:.................14x
Choose the correct option:
Fill in with he missing term:
(5x + 4)(5x – 7) = 25x2 + ................ - 28
= 25x2 - 28
a) 15x b) 55x
c) -3x d) -15x
Choose the correct option:
(-15x)
................- 15x
Fill in with the missing term:
(-3a - 7)(-3a – 2) = 9a2 + ................+ 14
a) 27a
b) 15a
c) -27a
d) -15a
Choose the correct option:
27a
(-2a + 8)(-2a – 4) = 4a2 + ................- 32
= 4a2 - 32
Fill in with the missing term:
(-8a)
a) -8a
b) 4a
c) 8a
d) 16a
Choose the correct option:
- 8a............
Fill in with the missing term:
(5p + 7q)2 = 25p2 + .......... + 49q2
(-2a + 5b)2 = 4a2 + ........... + 25b2
= 4a2 + 25b2
( -3f - 8g)2 = 9f2 + ............. +64g2
70pq
(-20ab)
48fg
.................- 20ab
Find the missing term in the following equation:
........9
16169
)3
44
3(
222
yxyx ?
a) 2xy b) -2xy
c) 12xy d) -12xy
ANS: ............................a) 2xy
Choose the correct option:
Fill in with the missing term:
a)
= + + ab b)
= +
..........(2
)127
)7
6()
127
76
(22
baba
a2
49
36 b14449
2
ab
)32
43
(2
xy
yx
.............. .............. ...........+ +yx
16
92
2
x
y
9
42
2
(-xy)
y
x
16
92
2
x
y
9
42
2
- xy............... ............ ..........
Fill in with the missing term:
= +
)165
58
(2
pq
qp
................. ................. .............qp
2516
2
2
pq
25625
2
2
(-pq)+ +
................ ................. ................qp
2516
2
2
pq
25625
2
2
- pq
If 6x – 4y = 3 , xy = 2 , then :
36x2 + 16y2 = ................. 105
If (-15p – 4q) = -3 , pq = -1, then :
225p2 + 16q2 = .................129
If (3a + 5b) = - 4 , 9a2 + 25b2 = -14 , then :
ab= ..................01(one)
If 9m2 + 49n2 = -3 , mn = 2 , then:
3m + 7n = ............... 09
If 25a2 + 81b2 = 216 , ab = -4 ,
then:
5a – 9b = 24..............
If 4a2 + 144b2 = 48 , ab = -2 ,
then:
a – 6b = ............... 06
If 25x2 - 64y2 = -90 , and 5x + 8y =10 , then :
5x – 8y = ........................................-9
If 256x2 - 81y2 = 72, 16x - 9y = 12p
and 16x + 9y = 3q , then :
pq =................02
If , then :
x
x 2
2 1
91
x
x
...................79
61
x
xIf , then :
x
x 2
2 1................38
1421
2
2 x
x
x
x1
If , then :
................................12
3981
2
2 x
x
x
x1
.............20
If , then :
2271
2
2 x
x
x
x1
15.......................
If , then :
5311
2
2 x
x
x
x1
......................23
If , then :
Expand :
(3a + 2b)3 =
(4x + 7y)3 =
27a3................ + 54a2b + 36ab2 + 8b3
.............. ................ ............. ..........64x3 + 336x2y + 588xy2 + 343y3
................ ................ ................
(8y – 5x )3 =
(3b – 7a)3 =
..............512y3 - 960y2x................. - 125x3.............. + 600x2y..............
................27b3 ................ - 189b2a + 441ba2................ - 343a3..............
Expand :
(-2d + 7a)3 =
(-a - 6c)3 =
............. .......................................
....................................................
- 8d3 + 84d2a - 294da2 + 343a3
- a3 - 18a2c - 108ac2 - 216c3
Expand :