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Chapters
1: Rational and Irrational Numbers
UNIT-II: COMMERCIAL MATHEMATICS
2: Compound Interest
UNIT-III: ALGEBRA
▶ 3: Expansions
4: Factorisation
5: Simultaneous Linear Equations
6: Indices
7: Logarithms
UNIT-IV: GEOMETRY
8: Triangles
9: Inequalities
10: Mid-point Theorem
11: Pythagoras Theorem
12: Rectilinear Figures (Theorems on Parallelograms and Construction of Polygons)
13: Theorems on Area
14: Circles (Chord and Arc Properties)
UNIT-V: STATISTICS
15: Statistics
16: Graphical Representation of Statistical Data
UNIT-VI: MENSURATION
17: Mensuration
18: Surface Area and Volume of Solids
UNIT-VII: TRIGONOMETRY
19: Trigonometry
20: Simple 2-D Problems in Right Triangle
UNIT-VIII: COORDINATE GEOMETRY
21: Coordinate Geometry
![B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 3 - Expansions - Shaalaa.com](/images/mathematics-english-class-9-icse_6:a927b361d63845f4b2afea4ec6bbe35a.jpg "B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 3 - Expansions")
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Solutions for Chapter 3: Expansions
Below listed, you can find solutions for Chapter 3 of CISCE B Nirmala Shastry for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई.
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 3 Expansions EXERCISE A [Pages 32 - 33]
Expand the following:
(3a + 5b)2
Expand the following:
(4a − 7b)2
Expand the following:
`((2a)/(5b) - (5b)/(2a))^2`
Expand the following:
(2ab + 3cd)2
Expand the following:
(2a3 + 5b2)2
Expand the following:
(−2a − 5b)2
Evaluate using algebraic formula:
1042
Evaluate using algebraic formula:
992
Evaluate using algebraic formula:
10.22
Evaluate using algebraic formula:
9.72
Evaluate using algebraic formula:
992 + 2(99) + 1
Evaluate using algebraic formula:
4.82 + 2(4.8)(0.2) + (0.2)2
If a + b = 9 and ab = 18, find a − b.
If a − b = 5 and ab = 6, find a + b.
If `x+1/x = 4, "find" x^2+1/x^2`
If `x-1/x=8,"find" x^2+1/x^2`
If x + y = `5/2` and xy = 1, find x − y.
If 3x + 4y = 13 and xy = 1, find 3x − 4y.
If x2 − 4x = 1, find `x^2+1/x^2`.
If x2 − 8x + 1 = 0, find `x^2+1/x^2`.
If a2 + b2 = 65 and ab = 8, find the value of a2 − b2.
If 3x + 4y = 16 and xy = 4, find the value of 9x2 + 16y2.
If `x^2 + 1/x^2 = 51, "find" x - 1/x`
If `4x^2+1/(9x^2)=14 2/3, "find" (2x +1/(3x)).`
If `x^4+1/x^4=119, "find" x^2+1/x^2.`
If `x^4+1/x^4=119, "find" x-1/x`
If x − y = 5, xy = 84, find x + y.
If `(x^2 + 1)/x = 5, "find" x^2 + 1/x^2`
If `(x^2 - 1)/x = 7, "find" x^2 + 1/x^2`
Find the missing term in the following expression to make a perfect square.
`square+42x+9`
Find the missing term in the following expression to make a perfect square.
`4x^2-square+49`
Find the missing term in the following expression to make a perfect square.
`25x^2+40xy+square`
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 3 Expansions EXERCISE B [Pages 35 - 36]
Expand the following:
(2a + 3b)3
Expand the following:
(5a + 4b)3
Expand the following:
`(2a+1/a)^3`
Expand the following:
(5a − 3b)3
Expand the following:
(2a − 7b)3
Expand the following:
`(3a-1/a)^3`
Expand the following:
(5ab + 2)3
Expand the following:
(3 − 4ab)3
Expand the following:
`((3x)/4+(2y)/5)^3`
Expand the following:
`(3x-1/(3x))^3`
Answer the following:
If a + b = 6 and ab = 8, find: a3 + b3.
If a + b = 8 and ab = 15, find a3 + b3.
If 2x + 3y = 10, xy = 4, find 8x3 + 27y3.
Answer the following:
If a − b = 7, ab = 30, find a3 − b3.
If a – b = 9, ab = 10, find a3 – b3.
If a − 2b = 4, ab = 6, find a3 − 8b3.
Answer the following:
If `x+1/x = 2, "find" x^3+1/x^3.`
If `x + 3/x = 4, "find" x^3 + 27/x^3`.
If `3x + 1/(3x) = 7, "find" 27x^3 + 1/(27x^3)`
Answer the following:
If \[x - \frac{1}{x} = 5\], find the value of \[x^3 - \frac{1}{x^3}\]
If `x - 3/x = 4, "find" x^3 - 27/x^3`.
If `2x - 1/x = 1, "find" 8x^3 - 1/x^3`.
If x2 − 4x + 1 = 0, find `x+1/x`.
If x2 − 4x + 1 = 0, find `x^3 + 1/x^3`.
If x2 − 6x − 1 = 0, find `x-1/x`.
If x2 − 6x − 1 = 0, find `x^3-1/x^3`.
If `(x^2 + 1)/x = 7, "find" x + 1/x`.
If `(x^2 + 1)/x = 7, "find" x^3 + 1/x^3`.
If `(x^2 - 1)/x = 8, "find" x - 1/x`.
If `(x^2 - 1)/x = 8, "find" x^3 - 1/x^3`.
If `(x^2 + 1)/x = 3 1/3` and x > 1; Find `x - 1/x`.
If `(x^2 + 1)/x = 3 1/3` and x > 1; find If `x^3 - 1/x^3`
Find the value of ab and a2 + b2 in the following:
If a + b = 5 and a3 + b3 = 35
Find the value of ab and a2 + b2 in the following:
If a + b = 8 and a3 + b3 = 152
Find the value of ab and a2 + b2 in the following:
If a − b = 3 and a3 − b3 = 63
Find the value of ab and a2 + b2 in the following:
If a − b = 4 and a3 − b3 = 124
Find the value of ab and a3 + b3 in the following:
If a + b = 8, a2 + b2 = 34
Find the value of ab and a3 + b3 in the following:
If a + b = 9, a2 + b2 = 53
Find the value of ab and a3 − b3 in the following:
If a − b = 4, a2 + b2 = 40
Find the value of ab and a3 − b3 in the following:
If a − b = 7, a2 + b2 = 65
Evaluate using the formula:
793 + 3(79)2 + 3(79) + 1
Evaluate using the formula:
483 + 6(48)2 + 12(48) + 8
Without actually calculating the cubes, find the value of:
(–32)3 + (15)3 + (17)3
Without actually calculating the cubes, find the value of:
(25)3 + (–17)3 + (–8)3
If x + y + z = 0, prove that `(x + y)^2/(xy) + (y + z)^2/(yz) + (z + x)^2/(zx) = 3`
If `x=1/(3 - x),` find the value of `x + 1/x`.
If `x = 1/(3 - x),` find the value of `x^2 + 1/x^2`.
If `x = 1/(3 - x),` find the value of `x^3 + 1/x^3`
If `9x^2 + 1/(4x^2) = 13,` find the value of `3x + 1/(2x)`.
If `9x^2 + 1/(4x^2) = 13,` find the value of `27x^3 + 1/(8x^3)`
If `25x^2 + 1/(4x^2) = 20,` find the value of `5x + 1/(2x)`
If `25x^2 + 1/(4x^2) = 20,` find the value of `125x^3 + 1/(8x^3)`
If `x^4 + 1/x^4 = 194, "find" x^2 + 1/x^2`
If `x^4 + 1/x^4 = 194, "find" x+ 1/x`
If `x^4 + 1/x^4 = 194, "find" x^3 + 1/x^3`
If `x^4 + 1/x^4 = 527,` find the value of `x^2 + 1/x^2`
If `x^4 + 1/x^4 = 527,` find the value of `x + 1/x`
If `x^4 + 1/x^4 = 527,` find the value of `x^3 + 1/x^3`
Evaluate using algebraic formula:
1023
Evaluate using algebraic formula:
993
Evaluate using algebraic formula:
10.13
Evaluate using algebraic formula:
9.73
Evaluate using algebraic formula:
993 + 3(99)2 + 3(99) + 1
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 3 Expansions EXERCISE C [Page 38]
Use the direct method to evaluate the following products:
(x + 8)(x + 3)
Expand using the formula:
(x − 5) (x + 6)
Expand using the formula:
(a − 4)(a − 3)
Expand using the formula:
(a + 7) (a − 2)
Expand using the formula:
(3x + 5y + 2) (3x + 5y − 2)
Expand using the formula:
(4x + 2y + 3) (4x + 2y − 3)
Expand using the formula:
(2a + 3b + 5) (2a − 3b + 5)
Expand using the formula:
(4a + 5b − 7) (4a + 5b + 2)
Expand:
(2a − 3b + 5c)2
Expand:
(4a − 5b − 6)2
Expand:
`(a/2 + 2b - 4c)^2`
Expand:
`(5a - b/2 + 4c)^2`
If a + b + c = 7 and a2 + b2 + c2 = 45, find the value of ab + bc + ca.
If a + b + c = 9 and ab + bc + ca = 14, find the value of a2 + b2 + c2.
If ab + bc + ca = 27 and a2 + b2 + c2 = 90, find the value of a + b + c.
If a2 + b2 + c2 = 29 and ab + bc + ca = 26, find the value of a + b + c.
If a2 + b2 + c2 = 74 and ab + bc + ca = 61, find the value of a + b + c.
If ab + bc + ca = 31 and a2 + b2 + c2 = 38, find the value of a + b + c.
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 3 Expansions MULTIPLE CHOICE QUESTIONS [Pages 38 - 39]
If a + b = 8, ab = 7 then a2 + b2 = ______.
64
78
50
49
If `x + 1/x = 3, "then" x^2 + 1/x^2` = ______.
9
7
11
12
If a − b = 8, ab = 20 then a2 + b2 = ______.
62
104
66
96
If `x + 1/x = 4, "then" x^3 + 1/x^3 =` ______.
52
76
64
62
If `x - 1/x = 5, "then" x^3 - 1/x^3 =` ______.
110
140
125
127
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
0
abc
3abc
2abc
61 × 59 = ______.
3,600
3,599
3,609
3,509
782 − 222 = ______.
5,600
6,600
5,700
5,900
`a = 1/(a - 2). ∴ a - 1/a=` ______.
4
3
2
1
`(a^2 + 1)/a - 5 = 0 ∴ a + 1/a =` ______.
5
25
10
6
a + b + c = 6, ab + bc + ac = 11 ∴ a2 + b2 + c2 = ______.
25
14
47
58
a2 + b2 + c2 = 42, ab + bc + ac = 29 ∴ a + b + c = ______.
16
14
12
10
a2 + b2 + c2 = 35, a + b + c = 9 ∴ ab + bc + ac = ______.
15
20
23
25
a − b = 3, a2 + b2 = 29. ∴ ab = ______.
19
10
18
12
(x + 5) (x − 4) = ______.
x2 + x − 20
x2 − x − 20
x2 + x + 20
x2 + 9x − 20
(x − 3) (x − 2) = ______.
x2 + 5x − 6
x2 + x − 6
x2 − 5x + 6
x2 − x − 6
a + b = 10, ab = 24 ∴ a3 + b3 = ______.
280
270
1720
520
ab = 36, a − b = 9 ∴ a3 − b3 = ______.
243
1701
729
765
a2 + b2 + c2 = 66, ab − bc − ca = 17 ∴ a + b − c = ______.
12
11
9
10
592 + 2 × 59 + 1 = ______.
4800
3600
2500
4900
Which of the following is a factor of (x + y)3 – (x3 + y3)?
x2 + y2 + 2xy
x2 + y2 – xy
xy2
3xy
In each of the following questions, a statement of assertion (A) is given and a statement of Reason (R) given below it choose the correct option for each question.
Assertion (A): If `x + 1/x = 5, "then" x^3 + 1/x^3 = 125`
Reason (R): `(x + 1/x)^3 = x^3 + 1/x^3 + 3(x + 1/x)`
Both A and R are true, and R is the correct reason for A.
Both A and R are true, but R is the incorrect reason for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A): If 2a − 3b = 10, ab = −4 then 8a3 − 27b3 = 280
Reason (R): (2a − 3b)3 = 8a3 − 27b3 − 18ab (2a − 3b)
Both A and R are true, and R is the correct reason for A.
Both A and R are true, but R is the incorrect reason for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A): If (x + b)2 = x2 − 16x + a, then a = 64, b = −8
Reason (R): (a − b)2 = a2 − 2ab + b2
Both A and R are true, and R is the correct reason for A.
Both A and R are true, but R is the incorrect reason for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A): a2 + b2 + c2 = 66, ab − bc − ca = 17 ∴ a + b − c = ±10
Reason (R): (a + b − c)2 = a2 + b2 − c2 + 2ab − 2bc − 2ca
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.
A is true, but R is false.
A is false, but R is true.
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई 3 Expansions MISCELLANEOUS EXERCISE [Pages 39 - 40]
Expand the following:
(5ab − 4cd)2
Expand the following:
(3x3 − 8y2)2
Expand the following:
(−6x − 7y)2
Expand the following:
(5x − 4y)3
Expand the following:
`(3x + 1/(3x))^3`
Expand the following:
(2a − 5b − 6c)2
Evaluate using algebraic formula:
983 + 6(98)2 + 12(98) + 23
If x2 − 9x + 1 = 0, find the value of `x+1/x and x^3 + 1/x^3.`
Given `x - 3/x = 5, "find the value of" x^3 - 27/x^3.`
If `9x^2 + 1/(4x^2) = 13,` find the value of `3x + 1/(2x)`.
If `9x^2 + 1/(4x^2) = 13,` find the value of `27x^3 + 1/(8x^3)`
If `x^4 + 1/x^4 = 2, "find the value of" x^2 + 1/x^2, x + 1/xandx^3 + 1/x^3.`
Find the product:
(5x + 4y + 2) (5x + 4y − 2)
If a − b = 2, ab = 15, find a + b.
If a − b = 2, ab = 15, find a3 − b3.
Without calculating the cubes, find the value of (25)3 + (–12)3 + (–13)3.
If x2 + y2 = 34 and xy = `10 1/2`, find the value of 2(x + y)2 + (x − y)2.
If 2a + 5b = 11, ab = 3, find the value of 8a3 +125b3.
If a + b = 7 and a3 + b3 = 91, find the value of ab.
If a2 + b2 + c2 = 26 and a + b + c = 8, find the value of ab + bc + ca.
If a2 + b2 + c2 = 65 and ab + bc + ca = 8, find the value of a + b + c.
If 5x − 4y = 6 and xy = 2, find the value of 125x3 − 64y3.
Solutions for 3: Expansions
B Nirmala Shastry solutions for मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 3 - Expansions
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Concepts covered in मॅथेमॅटिक्स [इंग्रजी] इयत्ता ९ आयसीएसई chapter 3 Expansions are Algebraic Identities, Expansion of Formula, Special Product, Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method, Expansion of (a + b)3.
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