RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 5. Factorization of Algebraic Expressions

Subject: Mathematics - Class 9th

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Chapter Exercises

Exercise 5.1
Exercise 5.2
Exercise 5.3
Exercise 5.4
CCE - Formative Assessment

Exercise 5.1

1

Factorize:

x3+x-3x2-3
2

Factorize:

a(a+b)3-3a2b(a+b)
3

Factorize:

x(x3–y3)+3xy-(x–y)
4

Factorize:

a2x2+(ax2+1)x+a
5

Factorize:

x2+y-xy-x
6

Factorize:

x3-2x2y+3xy2-6y3
7

Factorize:

6ab-b2+12ac-2bc
8

Factorize:
9

Factorize:

x(x–2)(x–4)+4x-8
10

Factorize:

(x+2)(x2+25)-10x2-20x
11

Factorize:

2a2+2ab+3b2
12

Factorize:

(a-b+c)2+(b-c+a)2+2(a-b+c)(b-c+a)
13

Factorize:

a2+b2+2(ab+bc+ca)
14

Factorize:

4(x-y)2-12(x-y)(x+y)+9(x+y)2
15

Factorize:

a2-b2+2ab-c2
16

Factorize:

a2+2ab+b2-c2
17

Factorize:

a2+4b2-4ab-4c2
18

Factorize:

xy9–yx9
19

Factorize:

x4+x2y2+y4
20

Factorize:

x2-y2-4xz+4z2
21

Factorize:

x2+6x+10
22

Factorize:

x2-2x-30
23

Factorize:

x2-x-6
24

Factorize:

x2+5x+30
25

Factorize:

x2+2x-24
26

Factorize:

2x2-x+
27

Factorize:

x2+x+
28

Factorize:

21x2-2x+
29

Factorize:

5x2+20x+3
30

Factorize:

2x2+3x+531.9(2a-b)2-4(2a-b)-13
31

Factorize:

9(2a – b)2 –4 (2a – b) – 13
32

Factorize:

7(x-2y)2-25(x-2y)+12
33

Factorize:

2(x+y)2-9(x+y)-5
34

Give possible expressions for the length and breadth of the rectangle having 35y2+13y-12 as its area.
35

What are the possible expressions for the dimensions of the cuboid whose volume is 3x2-12x.

Exercise 5.2

1

Factorize each of the following expressions:

p3+27
2

Factorize each of the following expressions:

y3+125
3

Factorize each of the following expressions:

1-27a3
4

Factorize each of the following expressions:

8x3y3+27a3
5

Factorize each of the following expressions:

64a3-b3
6

Factorize each of the following expressions:

-8y3
7

Factorize each of the following expressions:

10x4y-10xy4
8

Factorize each of the following expressions:

54x6y+2x3y4
9

Factorize each of the following expressions:

32a2+108b3
10

Factorize each of the following expressions:

(a-2b)3-512b3
11

Factorize each of the following expressions:

(a+b)3-8(a+b)3
12

Factorize each of the following expressions:

(x+2)3+(x-2)3
13

Factorize each of the following expressions:

8x2y3-x5
14

Factorize each of the following expressions:

1029-3x3
15

Factorize each of the following expressions:

x6+y6
16

Factorize each of the following expressions:

x3y3+1
17

Factorize each of the following expressions:

x4y4-xy
18

Factorize each of the following expressions:

a12+b12
19

Factorize each of the following expressions:

x3+6x2+12x+16
20

Factorize each of the following expressions:

a3+b3+a+b
21

Factorize each of the following expressions:

a3--2a
22

Factorize each of the following expressions:

a3+3a2b3+3ab2+b3-8
23

Factorize each of the following expressions:

8a3-b3-4ax+2bx
24

Simplify

(i)


(ii)


(iii)

Exercise 5.3

1

Factorize:

64a3+125b3+240a2b+300ab2
2

Factorize:

125x3-27y3-225x2y+125xy2
3

Factorize:

x3+1+x2+2x
4

Factorize:

8x3+27y3+36x2y+54xy2
5

Factorize:

a3-3a2b+3ab2-b3+8
6

Factorize:

x3+8y3+6x2y+12xy2
7

Factorize:

8x3+y3+12x2y+6xy2
8

Factorize:

8a3+27b3+36a2b+54ab2
9

Factorize:

8a3-27b3-36a2b+54ab2
10

Factorize:

x3-12x(x-4)-64
11

Factorize:

a3x3-3a2bx2+3ab2x-b3

Exercise 5.4

1

Factorize each of the following expressions:

a3+8b3+64c3-24abc
2

Factorize each of the following expressions:

x3-8y3+27z3+18xyz
3

Factorize each of the following expressions:

27x3-y3-z3-9xyz
4

Factorize:

x3-y3+125z3+5xyz
5

Factorize each of the following expressions:

8x3+27y3-216z3+108xyz
6

Factorize each of the following expressions:

125+8x3-27y3+90xy
7

Factorize:

(3x-2y)3+(2y-4z)3+(4z-3x)3
8

Factorize each of the following expressions:

(2x-3y)3+(4z-2x)3+(3y-4z)3
9

Factorize each of the following expressions:
10

Factorize each of the following expressions:

(a-3b)3+(3b-c)3+(c-a)3
11

Factorize each of the following expressions:

2a3+3b3+c3-3abc
12

Factorize each of the following expressions:

3a3-b3-5c3-3abc
13

Factorize each of the following expressions:

8x3-125y3+180xy+216
14

Factorize each of the following expressions:

2a3+16b3+c3-12abc
15

Find the value of x3+y3-12xy+64,whenx+y=-4.
16

Multiply:

(i) x2+y2+z2-xy+xz+yzbyx+y-z


(ii) x2+4y2+z2+2xy+xz-2yzbyx-2y-z


(iii) x2+4y2+2xy+-3x+6y+9byx-2y+3


(iv) 9x2+25y2+15xy+12x-20y+16by3x-5y+4

CCE - Formative Assessment

1

Factorize: x4+x2+25.
2

Factorize: x2-1-2a–a2.
3

If a + b + c = 0, then write the value of a3+b3+c3.
4

Ifa2+b2+c2=20,anda+b+c=0,findab+bc+ca.
5

If a + b + c = 9 and ab + bc + ca = 40, find a2 + b2 + c2.
6

If a2 + b2 + c2 = 250 and ab + bc + ca = 3, find a + b + c.
7

Write the value of: 253–753+503.
8

Write the value of: 483–303-183.
9

Write the value of:
10

Write the value of: 303+203-503.
1

The factors of a2-1-2x-x2 are
2

The factors of x4+x2=25 are
3

The factors of x2+4y2+4y-4xy-2x-8 are
4

The factors of x3-x2y-xy2+y3are
5

The factors of x3-1+y3+3xyare
6

The factors of 8a2+b3-6ab+1are
7

(x+y)3-(x-y)3 can be factorized as:
8

The factors of x2-7x+6are
9

The expression (a-b)3+(b-c)3+(c-a)3 can be factorized as:
10

The expression x4+4 can be factorized as
11

If 3x=a+b+c, then the value of (x-a)3+(x-b)3+(x-c)3-3(x-a)(x-b)(x-c) is
12

If (x+y)3-(x-y)3-6y(x2-y2)=ky2 then k=
13

Ifx3-3x2+3x-7=(x+1)(ax2+bx+c), then a+b+c=
14

The value ofis
15

The value of is