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Chapters
2: Compound Interest
▶ 3: Expansions
4: Factorisation
5: Simultaneous Linear Equations
6: Indices/Exponents
7: Logarithms
8: Triangles
9: Mid-point Theorem
10: Pythagoras Theorem
11: Rectilinear Figures
12: Constructions of Polygons
13: Theorems on Area
14: Circles
15: Statistics
16: Mensuration
17: Trigonometric Ratios
18: Trigonometric Ratios of Some Standard Angles and Complementary Angles
Chapter 19: Co-ordinate Geometry: An Introduction
![Nootan solutions for Mathematics [English] Class 9 ICSE chapter 3 - Expansions - Shaalaa.com](/images/mathematics-english-class-9-icse_6:f26eb985e8254aa987299226050d7c71.jpg "Nootan solutions for Mathematics [English] Class 9 ICSE chapter 3 - Expansions")
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Solutions for Chapter 3: Expansions
Below listed, you can find solutions for Chapter 3 of CISCE Nootan for Mathematics [English] Class 9 ICSE.
Nootan solutions for Mathematics [English] Class 9 ICSE 3 Expansions Exercise 3A [Pages 64 - 65]
Expand the following:
(x + 3y)2
Expand the following:
(3x – 2y)2
Expand the following:
`(1/3x + 1/2y)^2`
Expand the following:
`(2x - 1/3 y)^2`
Expand the following:
(3x + y – 5z)2
Expand the following:
`(x/2 - (3y)/5 + z)^2`
Expand the following:
`(5x + 1/x)^2`
Expand the following:
`(3x - 1/(2x))^2`
Find the product:
(x + 1) (x + 5)
Find the product:
(x + 2) (х – 6)
Find the product:
(x – 4) (х – 6)
Find the product:
(3x + 1) (3x + 5)
Find the product:
(За – 2b) (3a + 2b)
Find the product:
(5x + 3y) (5x – 3y)
Find the product:
(x + 2y + 3) (x + 2y – 3)
Find the product:
`(x - 1/x + 4)(x - 1/x - 4)`
Find the product:
(3x + y + 2) (3x – y + 2)
Find the product:
(x + 2) (x − 2) (x2 + 4)
Expand the following:
(x + 3y + 2) (x + 3y + 5)
Expand the following:
(2x – 3y + 1) (2x – 3y – 5)
Expand the following:
(2x + 3y)3
Expand the following:
(3a + b)3
Expand the following:
`(2x + 1/x)^3`
Expand the following:
`(2x + 1/(2x))^3`
Expand the following:
(3x – 5y)3
Expand the following:
(x – 3y)3
Expand the following:
`(3x - 1/x)^3`
Expand the following:
`(3x-1/(3x))^3`
Simplify the following:
(2a + b)2 + (2a – b)2
Simplify the following:
(a + 5b)2 – (a – 5b)2
Simplify the following:
(a + b)3 + (a – b)3
Simplify the following:
(2x + 5y)3 – (2x – 5y)3
Expand the following:
(x + y + 1)3
Expand the following:
(x – 2y + 3)3
Find the product:
(3x + y) (9x2 – 3xy + y2)
Find the product:
(x + 5y) (x2 – 5xy + 25y2)
Find the product:
(3x – 2y) (9x2 + 6xy + 4y2)
Find the product:
`(a - 1/a)(a^2 + 1/a^2 + 1)`
Simplify the following:
(a + 2b) (a2 – 2ab + 4b2) + (a – 2b) (a2 + 2ab + 4b2)
Simplify the following:
(3x + 5y) (9x2 – 15xy + 25y2) – (3x – 5y) (9x2 + 15xy + 25y2)
Find the product:
(x + 3) (x + 5) (x + 7)
Find the product:
(x – 1) (x + 3) (x + 2)
Find the coefficient of x and constant term in the product (x + 3) (x + 4) (x + 5).
Find the coefficient of x2 in the product (x – 1) (x – 5) (x – 6).
Using suitable identity, find the value of 1022.
Using suitable identity, find the value of 982.
Using suitable identity, find the value of (10.5)2.
Using suitable identity, find the value of 1013.
Using suitable identity, find the value of 983.
Using suitable identity, find the value of (1.1)3.
Find the product:
(3a + b + 5c) (9a2 + b2 + 25c2 – 3ab – 5bc – 15ас)
Find the product:
(x – 2y + 5z) (x2 + 4y2 + 25z2 + 2xy + 10yz – 5xz)
Find the product:
(За – 4b – c) (9a2 + 16b2 + c2 + 12ab – 4bc + 3ca)
Simplify:
(3x – 4y)3 + (4y – 5z)3 + (5z – 3x)3
Simplify:
(a – 4b)3 + (4b – 3c)3 + (3c – а)3
Without actually calculating the cube, find the value of the following:
(35)3 + (–15)3 + (–20)3
Without actually calculating the cube, find the value of the following:
`(-8/15)^3 + (1/3)^3 + (1/5)^3`
Using suitable identity, evaluate the following:
`(92 xx 92 xx 92 + 8 xx 8 xx 8)/(92 xx 92 - 92 xx 8 + 8 xx 8)`
Using suitable identity, evaluate the following:
`((103)^3 - (3)^3)/((103)^2 + 103 xx 3 + (3)^2)`
If a + b + 2c = 0, then prove that a3 + b3 + 8c3 = 6abc.
If x + 2y – 5 = 0, then prove that x3 + 8y3 + 30xy = 125.
If 4x – 5y – 2 = 0, then prove that 64x3 – 125y3 – 120xy = 8.
If 4x + 2y + z = 0, show that `((4x + 2y)^2)/(xy) + (2(4x + z)^2)/(xz) + (4(2y + z)^2)/(zx) = 24`.
If `(2a)/(3b) = (3b)/(4c)`, show that (2a – 3b + 4c) (2a + 3b + 4c) = 4a2 + 9b2 + 16c2.
Nootan solutions for Mathematics [English] Class 9 ICSE 3 Expansions Exercise 3B [Pages 71 - 73]
If x + y = 10 and xy = 21, find the value of x2 + y2.
If x – y = 6 and xy = 27, find the value of x2 + y2.
If 5a – b = 9 and ab = 2, find the value of 25a2 + b2.
If 3x + 2y = 13 and xy = 6, find the value of 9x2 + 4y2.
If x + y = 7 and x – y = 2, find the value of x2 + y2.
If x + y = 7 and x – y = 2, find the value of xy.
If x2 + y2 = 58 and xy = 21, find the value of x + y.
If x2 + y2 = 58 and xy = 21, find the value of x – y.
If x + y = 6 and xy = 8, find the value of x – y.
If x + y = 6 and xy = 8, find the value of x2 + y2.
If x + y = 6 and xy = 8, find the value of x3 + y3.
If a – b = 2 and ab = 3, find the value of a + b.
If a – b = 2 and ab = 3, find the value of a2 + b2.
If a – b = 2 and ab = 3, find the value of a3 + b3.
If `x + 1/x = 3`, find the value of `x^2 + 1/x^2`.
If `x - 1/x = 2`, find the value of `x + 1/x`.
If `x - 1/x = 2`, find the value of `x^2 + 1/x^2`.
If `x + 1/x = 5`, find the value of `x - 1/x`.
If `x + 1/x = 5`, find the value of `x^2 + 1/x^2`.
If `x + 1/x = 5`, find the value of `x^4 + 1/x^4`.
If `x + 1/x = 4`, find the value of `x^2 + 1/x^2`.
If `x + 1/x = 4`, find the value of `x^3 + 1/x^3`.
If `x - 1/x = 7` then find the value of `x^2 + 1/x^2`.
If \[x - \frac{1}{x} = 7\], find the value of \[x^3 - \frac{1}{x^3}\].
If `x - 1/x = 7`, find the value of `x^4 + 1/x^4`.
If `x - 1/x = 4`, find the value of `x^2 + 1/x^2`.
If `x - 1/x = 4`, find the value of `x^3 - 1/x^3`.
If x2 – 6x + 1 = 0, find the value of `x^2 + 1/x^2`.
If x2 – 6x + 1 = 0, find the value of `x^3 + 1/x^3`.
If x2 – 6x + 1 = 0, find the value of `x^4 + 1/x^4`.
If `x - 2/x = 2`, find the value of `x^3 - 8/x^3`.
If `x^2 + 1/x^2 = 23`, find the value of `x + 1/x`.
If `x^2 + 1/x^2 = 23`, find the value of `x^4 + 1/x^4`.
If `x^2 + 1/x^2 = 27`, find the value of `x - 1/x`.
If `x^2 + 1/x^2 = 27`, find the value of `x^4 + 1/x^4`.
If `a = 1/(4 - a)`, find the value of `a^2 + 1/a^2`.
If `a = 1/(4 - a)`, find the value of `a^3 + 1/a^3`.
If `x = 3 + 2sqrt(2)`, find the value of `1/x`.
If `x = 3 + 2sqrt(2)`, find the value of `x + 1/x`.
If `x = 3 + 2sqrt(2)`, find the value of `x^2 + 1/x^2`.
If `x = 5 - 2sqrt(6)`, find the value of `1/x`.
If `x = 5 - 2sqrt(6)`, find the value of `x - 1/x`.
If `x = 5 - 2sqrt(6)`, find the value of `x^2 + 1/x^2`.
If `x = 7 + 4sqrt(3)`, find the value of `1/x`.
If `x = 7 + 4sqrt(3)`, find the value of `x + 1/x`.
If x = `(7 + 4sqrt(3))`, find the value of `x^3 + (1)/x^3`.
If `x = 3 + 2sqrt(2)`, find the value of `sqrt(x) + 1/sqrt(x)`.
If x + y + z = 6, x2 + y2 + z2 = 14, find the value of xy + yz + zx.
If x + y – z = 0, xy – yz – zx = –8, find the value of x2 + y2 + z2.
If a – b + c = 4, ab + bc – ac = 17, find the value of a2 + b2 + c2.
If a2 + b2 + c2 = 38 and ab + bc + ca = 13, find the value of a + b + c.
If x – y = 2 and x2 + y2 = 34, find the value of xy.
If x – y = 2 and x2 + y2 = 34, find the value of x3 – y3.
The sum of two numbers is 10 and the sum of their squares is 68. Find the product of the numbers.
The sum of two numbers is 5 and the sum of their cubes is 35. Find the product of the numbers.
The number x is 4 more than the number y and their product is 21. Find the sum of the squares of two numbers.
Nootan solutions for Mathematics [English] Class 9 ICSE 3 Expansions Exercise 3C [Pages 73 - 75]
Multiple Choice Questions Choose the correct answer from the given four options in each of the following questions:
96 × 104 is equal to ______.
9974
9964
9984
9994
If x + y = 11 and xy = 30 then x2 + y2 is equal to ______.
61
56
58
65
If `a/b + b/a = 1` then the value of a3 + b3 is ______.
–1
0
1
2
The value of 1022 – 982 is ______.
600
2400
1600
800
If x – y = 1 and xy = 2, then the value of x3 – y3 is ______.
5
6
7
8
If `x + 1/x = 9`, then the value of `x^2 + 1/x^2` is ______.
77
79
83
85
If `x - 1/x = 3`, then the value of `x^3 - 1/x^3` is ______.
27
36
45
18
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
0
abc
3abc
2abc
The value of 883 + 123 – 1003 is equal to ______.
3abc
2abc
abc
0
If a + b + c = 16 and ab + bc + ca = 40 then a2 + b2 + c2 is equal to ______.
136
156
176
196
Assertion-Reason Type Questions In the following questions, a statement of Assertion (A) and a statement of Reason (R) are given:
Assertion: 98 × 102 = 9996
Reason: (a + b)(a – b) = a2 – b2
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Assertion: x + y = 8, xy = 15 then x2 + y2 = 34
Reason: x2 + y2 – 2xy = (x – y)2
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Assertion: (2x – y)3 = 8x3 + 12x2y + 6xy2 – y3
Reason: (a – b)3 = a3 – 3a2b + 3ab2 – b3
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Assertion: 183 + (–10)3 + (–8)3 = 4320
Reason: (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Valid Statements Questions In the following questions, two statements (i) and (ii) are given. Choose the valid statement.
(i) lf a + b + c = 0 then a3 + b3 + c3 = 0
(ii) If `x - 1/x = 3` then `x^3 - 1/x^3 = 36`
Only (i)
Only (ii)
Both (i) and (ii)
Neither (i) nor (ii)
(i) lf x – y = 2 and x2 + y2 = 34 then xy = 15
(ii) (a + b)2 = a2 + 2ab + b2
Only (i)
Only (ii)
Both (i) and (ii)
Neither (i) nor (ii)
(i) If x2 – 6x + 1 = 0 then `x^2 + 1/x^2 = 34`
(ii) x3 + y2 = (x + y)(x2 + xy + y2)
Only (i)
Only (ii)
Both (i) and (ii)
Neither (i) nor (ii)
(i) (x + y + 1)(x – y – 1) = x2 + (y + 1)2
(ii) (x + 9y)(x – 9y) = x2 – 9y2
Only (i)
Only (ii)
Both (i) and (ii)
Neither (i) nor (ii)
Solutions for 3: Expansions
Nootan solutions for Mathematics [English] Class 9 ICSE chapter 3 - Expansions
Shaalaa.com has the CISCE Mathematics Mathematics [English] Class 9 ICSE CISCE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. Nootan solutions for Mathematics Mathematics [English] Class 9 ICSE CISCE 3 (Expansions) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. Nootan textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.
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