Hg
Name: Class 9 Date:
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
fb.me/thehgclasses linkedin.com/company/the-hg-classes instagram.com/the_hg_classes g.page/the-hg-classes-gurugram thehgclasses.co.in
Polynomials - 4
1. Find the continued product (using suitable identities):
i) (2x + 3y)(2x – 3y) ii)
iii) (x - 1)(x + 1)(x
2
+ 1)(x
4
+ 1)
iv) (x -
- 1)(x +
+ 1) ** [Hint: Take -ve common from last 2 terms of 1st factor; then use identity a
2
– b
2
= (a + b)(a - b)]
2. Evaluate suitable identities:
i) 103 x 97 ii) 103 x 107 iii) (0.99)
2
iv) 185 x 185 – 115 x 115
v) (1002)
3
vi) (999)
3
vii) 30
3
+ 20
3
– 50
3
viii) (-12)
3
+ 7
3
+ 5
3
3. If x +
= 6, find: i) x
2
+
ii) x
3
+
iii) x
4
+
iv) x
6
+
v) x -
4. If x -
= -1, find: i) x
2
+
ii) x
3
-
iii) x
4
+
iv) x
6
+
v) x +
5. If x + y = 12 and xy = 32, find the value of x
2
+ y
2
.
6. If 4x
2
+ y
2
= 40 and xy = 6, find the value of 2x + y.
7. If a
2
+ b
2
+ c
2
= 20 and a + b + c =0, find ab + bc + ca.
8. If ab + bc + ca = 40 and a + b + c = 9, find a
2
+ b
2
+ c
2
.
9. If a + b = 10 and a
2
+ b
2
= 58, find a
3
+ b
3
. ** [Hint: find ab first similar to Q5, then use identify of a
3
– b
3
]
10. If x
2
+
= 83, find i) x
3
-
ii) x -
iii) x +
11. If x
4
+
= 194, find i) x
3
+
ii) x
2
+
iii) x +
iv) x -
12. If a + b = 10 and ab = 16, find the value of a
2
- ab + b
2
and a
2
+ ab + b
2
.
13. If a + b + c = 6 and a
2
+ b
2
+ c
2
= 11, prove that a
3
+ b
3
+ c
3
– 3abc = -9.
14. If x + y + z = 1, xy + yz + zx = -1, xyz = -1, prove that x
3
+ y
3
+ z
3
= 1.
15. Factorize:
i) a
2
- b
2
- a - b
v) x
4
+ 4 **
ix) 2x
2
– 9x -5
ii) x(x + z) -y(y + z) **
vi) x
2
+ 3
x + 6 **
x) 8x
2
+ 2xy – 15y
2
iii) x
4
+ x
2
+ 1 **
vii) 4
x
2
+ 5x – 2
**
xi) 25a
2
– 35a + 12
iv) x
4
+ 5x
2
+ 9 **
viii) 9x
2
– 4x – 13
xii) 27a
3
+ 125b
3
a) (x + 1)
3
– (x - 1)
3
**
b) x
9
– y
9
c) x
3
/216 – 8y
3
d) x
6
– 7x
3
– 8 **
e) a
3
+ 3a
2
b + 3ab
2
+ b
3
– 8 **
f) a
3
– 8b
3
– 64c
3
– 24abc
g) (x - y)
3
+ (y - z)
3
+ (z - x)
3
**
h) 2kx
2
+ 6kx – 20k
i) a
2
– b
2
+ 2bc – c
2
**
j) a
2
+ b
2
+ 2ab +2bc + 2ca **
k) 7x
2
- 25x + 12
Hg
Name: Class 9 Date:
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
fb.me/thehgclasses linkedin.com/company/the-hg-classes instagram.com/the_hg_classes g.page/the-hg-classes-gurugram thehgclasses.co.in
Answers:
1. i) 4x
2
– 9y
2
ii) x
8
-
iii) x
8
– 1 iv) x
2
– y
2
/25 – 1 – 2y/5
2. i) 9991 ii) 11021 iii) 0.9801 iv) 21000 v) 1,00,60,12,008
vi) 99,70,02,999 vii) -90,000 viii) -1260
3. i) 34 ii) 198 iii) 1,154 iv) 39,202 v) ±
4. i) 3 ii) -4 iii) 7 iv) 18 v) ±
5. 80
6. ±8
7. -10
8. 1
9. 370
10. i) 756 ii) ±9 iii) ±
11. i) 52 ii) 14 iii) 4 iv)
12. 52, 84
13. -9
14. 1
15. i) (a + b)(a – b – 1) ii) (x – y)(x + y + z) iii) (x
2
– x + 1)( x
2
+ x + 1)
iv) (x
2
– x + 3)( x
2
+ x + 3) v) (x
2
–
x + 2)( x
2
+
x + 2) vi) (x + 2
)(x +
)
vii) (
x + 2)(4x -
) viii) (x + 1)(9x - 13) ix) (a - 5)(2a + 1)
x) (2x + 3y)(4x - 5y) xi) (5a - 4)(5a - 3) xii) (3a + 5b)(9a
2
+ 15ab + 25b
2
)
a) 2x(x
2
+ 3) b) (x - y)(x
2
+ xy + y
2
)(x
6
+ x
3
y
3
+ y
6
)
c) (x/6 – 2y)(x
2
/36 + xy/3 + 4y
2
) d) (x - 2)(x + 1)(x
2
+ 2x + 4)(x
2
– x + 1)
e) (a + b - 2){(a + b)
2
+ 2(a + b) + 4} f) (a -2b – 4c)(a
2
+ 4b
2
+ 16c
2
+ 2ab – 8bc + 4ca)
g) 3(x - y)(y - z)(z - x) h) 2k(x - 2)(x + 5)
i) (a + b - c)(a – b + c) j) (a + b)(a + b + 2c)
k) (x - 3)(7x - 4)
