ICSE Class 9CISCE
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Selina solutions for Class 9 chapter 4 - Expansions (Including Substitution)

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Chapters

Chapter 1: Rational and Irrational Numbers

Chapter 2: Compound Interest (Without using formula)

Chapter 3: Compound Interest (Using Formula)

Chapter 4: Expansions (Including Substitution)

Chapter 5: Factorisation

Chapter 6: Simultaneous (Linear) Equations (Including Problems)

Chapter 7: Indices (Exponents)

Chapter 8: Logarithms

Chapter 9: Triangles [Congruency in Triangles]

Chapter 10: Isosceles Triangles

Chapter 11: Inequalities

Chapter 12: Mid-point and Its Converse [ Including Intercept Theorem]

Chapter 13: Pythagoras Theorem [Proof and Simple Applications with Converse]

Chapter 14: Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]

Chapter 15: Construction of Polygons (Using ruler and compass only)

Chapter 16: Area Theorems [Proof and Use]

Chapter 17: Circle

Chapter 18: Statistics

Chapter 19: Mean and Median (For Ungrouped Data Only)

Chapter 20: Area and Perimeter of Plane Figures

Chapter 21: Solids [Surface Area and Volume of 3-D Solids]

Chapter 22: Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals]

Chapter 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]

Chapter 24: Solution of Right Triangles [Simple 2-D Problems Involving One Right-angled Triangle]

Chapter 25: Complementary Angles

Chapter 26: Co-ordinate Geometry

Chapter 27: Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)

Chapter 28: Distance Formula

Selina Concise Class 9 Mathematics - Shaalaa.com

Chapter 4: Expansions (Including Substitution)

Exercise 4(A)Exercise 4(B)Exercise 4(C)Exercise 4(D)Exercise 4(E)

Selina solutions for Class 9 Chapter 4 Exercise Exercise 4(A) [Pages 57 - 58]

Exercise 4(A) | Q 1.1 | Page 57

Find the square of : 2a + b

Exercise 4(A) | Q 1.2 | Page 57

Find the square of : 3a + 7b

Exercise 4(A) | Q 1.3 | Page 57

Find the square of : 3a - 4b

Exercise 4(A) | Q 1.4 | Page 57

Find the square of : `(3a)/(2b) - (2b)/(3a)`

Exercise 4(A) | Q 2.1 | Page 57

Use identities to evaluate : (101)2

Exercise 4(A) | Q 2.2 | Page 57

Use identities to evaluate : (502)2

Exercise 4(A) | Q 2.3 | Page 57

Use identities to evaluate : (97)2

Exercise 4(A) | Q 2.4 | Page 57

Use identities to evaluate : (998)2

Exercise 4(A) | Q 3.1 | Page 57

Evalute : `( 7/8x + 4/5y)^2`

Exercise 4(A) | Q 3.2 | Page 57

Evalute : `((2x)/7 - (7y)/4)^2`

Exercise 4(A) | Q 4.1 | Page 58

Evaluate : `(a/[2b] + [2b]/a )^2 - ( a/[2b] - [2b]/a)^2 - 4`

Exercise 4(A) | Q 4.2 | Page 58

Evaluate : (4a +3b)2 - (4a - 3b)2 + 48ab.

Exercise 4(A) | Q 5 | Page 58

If a + b = 7 and ab = 10; find a - b.

Exercise 4(A) | Q 6 | Page 58

If a - b = 7 and ab = 18; find a + b.

Exercise 4(A) | Q 7 | Page 58

If x + y = `7/2  "and xy" =5/2`  ; find :  x - y  and x2 - y2

Exercise 4(A) | Q 8 | Page 58

If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a2 - b2.

Exercise 4(A) | Q 9 | Page 58

If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab

Exercise 4(A) | Q 10 | Page 58

If a + `1/a`= 6 and  a ≠ 0 find :
(i) `a - 1/a   (ii)  a^2 - 1/a^2`

Exercise 4(A) | Q 11 | Page 58

If a - `1/a`= 8 and  a ≠ 0 find :
(i) `a + 1/a   (ii)  a^2 - 1/a^2`

Exercise 4(A) | Q 12 | Page 58

If a2 - 3a + 1 = 0, and a ≠ 0; find : 
(i) `a + 1/a         (ii) a^2 + 1/a^2`

Exercise 4(A) | Q 13 | Page 58

If a2 - 5a - 1 = 0 and a ≠ 0 ; find :
(i) `a - 1/a`  
(ii) `a + 1/a`
(iii) `a^2 - 1/a^2`

Exercise 4(A) | Q 14 | Page 58

If 3x + 4y = 16 and xy = 4; find the value of 9x2 + 16y2.

Exercise 4(A) | Q 15 | Page 58

The number x is 2 more than the number y. If the sum of the squares of x and y is 34, then find the product of x and y.

Exercise 4(A) | Q 16 | Page 58

The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.

Selina solutions for Class 9 Chapter 4 Exercise Exercise 4(B) [Pages 60 - 61]

Exercise 4(B) | Q 1.1 | Page 60

Find the cube of : 3a- 2b

Exercise 4(B) | Q 1.2 | Page 60

Find the cube of : 5a + 3b

Exercise 4(B) | Q 1.3 | Page 60

Find the cube of : `2a + 1/(2a)`     ( a ≠ 0 )

Exercise 4(B) | Q 1.4 | Page 60

Find the cube of : `( 3a - 1/a )  (a ≠ 0 )`

Exercise 4(B) | Q 2 | Page 60

If  a2 + `1/a^2 = 47` and a ≠ 0   find :
(i) `a + 1/a`
(ii) `a^3 + 1/a^3`

Exercise 4(B) | Q 3 | Page 60

If  `a^2 + 1/a^2` = 18; a ≠ 0 find :

(i) `a - 1/a`

(ii) `a^3 - 1/a^3`

Exercise 4(B) | Q 4 | Page 60

If `a + 1/a` = p and a ≠ 0 ; then show that :

`a^3 + 1/a^3 = p(p^2 - 3)` 

Exercise 4(B) | Q 5 | Page 60

If a + 2b = 5; then show that : a3 + 8b3 + 30ab = 125.

Exercise 4(B) | Q 6 | Page 60

If `( a + 1/a )^2 = 3 "and a ≠ 0; then show" : a^3 + a^(1/3) = 0`

Exercise 4(B) | Q 7 | Page 60

If a + 2b + c = 0; then show that : a3 + 8b3 + c3 = 6abc.

Exercise 4(B) | Q 8.1 | Page 60

Use property to evaluate : 133 + (-8)3 + (-5)3

Exercise 4(B) | Q 8.2 | Page 60

Use property to evaluate : 73 + 33 + (-10)3

Exercise 4(B) | Q 8.3 | Page 60

Use property to evaluate : 93 - 53 - 43

Exercise 4(B) | Q 8.4 | Page 60

Use property to evaluate : 383 + (-26)3 + (-12)3

Exercise 4(B) | Q 9.1 | Page 60

If a ≠ 0 and `a - 1/a` = 3 ; find : 
`a^2 + 1/a^2`

Exercise 4(B) | Q 9.2 | Page 60

If a ≠ 0 and `a- 1/a` = 3 ; Find :
`a^3 - 1/a^3`

Exercise 4(B) | Q 10.1 | Page 60

If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^2 + 1/a^2 )`

Exercise 4(B) | Q 10.2 | Page 60

If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^4 + 1/a^4 )`

Exercise 4(B) | Q 10.3 | Page 60

If a ≠ 0 and `a - 1/a` = 4 ; find : `( a^3 - 1/a^3 )`

Exercise 4(B) | Q 11 | Page 61

If X ≠ 0 and X + `1/"X"` = 2 ; then show that :

`x^2 + 1/x^2 = x^3 + 1/x^3 = x^4 + 1/x^4`

Exercise 4(B) | Q 12 | Page 61

If 2x - 3y = 10 and xy = 16; find the value of 8x3 - 27y3.

Exercise 4(B) | Q 13.1 | Page 61

Expand : (3x + 5y + 2z) (3x - 5y + 2z)

Exercise 4(B) | Q 13.2 | Page 61

Expand : (3x - 5y - 2z) (3x - 5y + 2z)

Exercise 4(B) | Q 14 | Page 61

The sum of two numbers is 9 and their product is 20. Find the sum of their (i) Squares (ii) Cubes

Exercise 4(B) | Q 15 | Page 61

Two positive numbers x and y are such that x > y. If the difference of these numbers is 5 and their product is 24, find:
(i) Sum of these numbers
(ii) Difference of their cubes
(iii) Sum of their cubes.

Exercise 4(B) | Q 16 | Page 61

If 4x+ y= a and xy = b, find the value of 2x + y.

Selina solutions for Class 9 Chapter 4 Exercise Exercise 4(C) [Pages 62 - 63]

Exercise 4(C) | Q 1.1 | Page 62

Expand : ( x + 8 ) ( x + 10 )

Exercise 4(C) | Q 1.2 | Page 62

Expand : ( x + 8 )( x - 10 )

Exercise 4(C) | Q 1.3 | Page 62

Expand : ( X - 8 ) ( X + 10 )

Exercise 4(C) | Q 1.4 | Page 62

Expand : ( X - 8 )( X - 10 )

Exercise 4(C) | Q 2.1 | Page 62

Expand : `( 2x - 1/x )( 3x + 2/x )`

Exercise 4(C) | Q 2.2 | Page 62

Expand : `( 3a + 2/b )( 2a - 3/b )`

Exercise 4(C) | Q 3.1 | Page 62

Expand : ( x + y - z )2

Exercise 4(C) | Q 3.2 | Page 62

Expand : ( x - 2y + 2 )

Exercise 4(C) | Q 3.3 | Page 62

Expand : ( 5a - 3b + c )2

Exercise 4(C) | Q 3.4 | Page 62

Expand : ( 5x - 3y - 2 )2

Exercise 4(C) | Q 3.5 | Page 62

Expand : `( x - 1/x + 5)^2`

Exercise 4(C) | Q 4 | Page 63

If a + b + c = 12 and a2 + b2 + c2 = 50; find ab + bc + ca.

Exercise 4(C) | Q 5 | Page 63

If a2 + b2 + c2 = 35 and ab + bc + ca = 23; find a + b + c.

Exercise 4(C) | Q 6 | Page 63

If a + b + c = p and ab + bc + ca = q ; find a2 + b2 + c2.

Exercise 4(C) | Q 7 | Page 63

If a2 + b2 + c2 = 50 and ab + bc + ca = 47, find a + b + c.

Exercise 4(C) | Q 8 | Page 63

If x+ y - z = 4 and x2 + y2 + z2 = 30, then find the value of xy - yz - zx.

Selina solutions for Class 9 Chapter 4 Exercise Exercise 4(D) [Pages 64 - 65]

Exercise 4(D) | Q 1 | Page 64

If x + 2y + 3z = 0 and x3 + 4y3 + 9z3 = 18xyz ; evaluate : 
`[( x + 2y )^2]/(xy) + [(2y + 3z)^2]/(yz) + [(3z + x)^2]/(zx)`

Exercise 4(D) | Q 2.1 | Page 64

If a + `1/a` = m and a ≠ 0 ; find in terms of 'm'; the value of :
`a - 1/a`

Exercise 4(D) | Q 2.2 | Page 64

If a + `1/a` = m and a ≠ 0 ; find in terms of 'm'; the value of : 
`a^2 - 1/a^2`

Exercise 4(D) | Q 3.1 | Page 64

In the expansion of (2x2 - 8) (x - 4)2; find the value of
coefficient of x3

Exercise 4(D) | Q 3.2 | Page 64

In the expansion of (2x2 - 8) (x - 4)2; find the value of coefficient of x2

Exercise 4(D) | Q 3.3 | Page 64

In the expansion of (2x2 - 8) (x - 4)2; find the value of constant term.

Exercise 4(D) | Q 4 | Page 64

If x > 0 and `x^2 + 1/[9x^2] = 25/36, "Find"   x^3 + 1/[27x^3]` 

Exercise 4(D) | Q 5 | Page 64

If 2( x2 + 1 ) = 5x, find :
(i) `x - 1/x`

(ii) `x^3 - 1/x^3`

Exercise 4(D) | Q 6.1 | Page 64

If a2 + b2 = 34 and ab = 12; find : 3(a + b)2 + 5(a - b)2

Exercise 4(D) | Q 6.2 | Page 64

If a2 + b2 = 34 and ab = 12; find : 7(a - b)2 - 2(a + b)2

Exercise 4(D) | Q 7 | Page 64

If 3x - `4/x` = 4; and x ≠ 0 find : 27x3 - `64/x^3`

Exercise 4(D) | Q 8 | Page 64

If x2 + `x^(1/2)`= 7 and  x ≠ 0; find the value of : 
7x3 + 8x - `7/x^3 - 8/x`

Exercise 4(D) | Q 9 | Page 64

If x = `1/( x - 5 ) "and x ≠ 5. Find" : x^2 - 1/x^2`

Exercise 4(D) | Q 10 | Page 64

If x = `1/[ 5 - x ] "and x ≠ 5 find" x^3 + 1/x^3`

Exercise 4(D) | Q 11 | Page 64

If 3a + 5b + 4c = 0, show that : 27a3 + 125b3 + 64c3 = 180 abc

Exercise 4(D) | Q 12 | Page 64

The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their square.

Exercise 4(D) | Q 13.1 | Page 64

Find the value of 'a':  4x2 + ax + 9 = (2x + 3)2

Exercise 4(D) | Q 13.2 | Page 64

Find the value of 'a': 4x2 + ax + 9 = (2x - 3)2

Exercise 4(D) | Q 13.3 | Page 64

Find the value of 'a': 9x2 + (7a - 5)x + 25 = (3x + 5)2

Exercise 4(D) | Q 14.1 | Page 65

If `[x^2 + 1]/x = 3 1/3  "and x > 1; Find If" x - 1/x`

Exercise 4(D) | Q 14.2 | Page 65

If `[x^2 + 1]/x = 3 1/3  "and x > 1; Find If" x^3 - 1/x^3`

Exercise 4(D) | Q 15.1 | Page 65

The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : Their product

Exercise 4(D) | Q 15.2 | Page 65

The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : The sum of their squares

Selina solutions for Class 9 Chapter 4 Exercise Exercise 4(E) [Page 66]

Exercise 4(E) | Q 1.1 | Page 66

Simplify : ( x + 6 )( x + 4 )( x - 2 )

Exercise 4(E) | Q 1.2 | Page 66

Simplify : ( x - 6 )( x - 4 )( x + 2 )

Exercise 4(E) | Q 1.3 | Page 66

Simplify : ( x - 6 )( x - 4 )( x - 2 )

Exercise 4(E) | Q 1.4 | Page 66

Simplify : ( x + 6 )( x - 4 )( x - 2 )

Exercise 4(E) | Q 2.1 | Page 66

Simplify using following identity : `( a +- b )(a^2 +- ab + b^2) = a^3 +- b^3`
( 2x + 3y )( 4x2 + 6xy + 9y2 )

Exercise 4(E) | Q 2.2 | Page 66

Simplify using following identity : `( a +- b )(a^2 +- ab + b^2) = a^3 +- b^3`
`( 3x - 5/x )( 9x^2 + 15 + 25/x^2)`

Exercise 4(E) | Q 2.3 | Page 66

Simplify using following identity : `( a +- b )(a^2 +- ab + b^2) = a^3 +- b^3`
`(a/3 - 3b)(a^2/9 + ab + 9b^2)`

Exercise 4(E) | Q 3.1 | Page 66

Using suitable identity, evaluate (104)3

Exercise 4(E) | Q 3.2 | Page 66

Using suitable identity, evaluate (97)3 

Exercise 4(E) | Q 4 | Page 66

Simplify :
`[(x^2 - y^2)^3 + (y^2 - z^2)^3 + (z^2 - x^2)^3]/[(x - y)^3 + (y - z)^3 + (z - x)^3]`

Exercise 4(E) | Q 5.1 | Page 66

Evaluate :
`[0.8 xx 0.8 xx 0.8 + 0.5 xx 0.5 xx 0.5]/[0.8 xx 0.8 - 0.8 xx 0.5 + 0.5 xx .5]`

Exercise 4(E) | Q 5.2 | Page 66

Evaluate :
`[1.2 xx 1.2 + 1.2 xx 0.3 + 0.3 xx 0.3 ]/[ 1.2 xx 1.2 xx 1.2 -  0.3 xx 0.3 xx 0.3]`

Exercise 4(E) | Q 6 | Page 66

If a - 2b + 3c = 0; state the value of a- 8b3 + 27c3.

Exercise 4(E) | Q 7 | Page 66

If x + 5y = 10; find the value of x3 + 125y3 + 150xy - 1000.

Exercise 4(E) | Q 8 | Page 66

If x = 3 + 2√2, find :
(i) `1/x`

(ii) `x - 1/x`

(iii) `( x - 1/x )^3`

(iv) `x^3 - 1/x^3`

Exercise 4(E) | Q 9 | Page 66

If a + b = 11 and a2 + b2 = 65; find a3 + b3.

Exercise 4(E) | Q 10 | Page 66

Prove that :  x2+ y2 + z2 - xy - yz - zx  is always positive.

Exercise 4(E) | Q 11.1 | Page 66

Find : (a + b)(a + b)

Exercise 4(E) | Q 11.2 | Page 66

Find : (a + b)(a + b)(a + b)

Exercise 4(E) | Q 11.3 | Page 66

Find : (a - b)(a - b)(a - b)

Chapter 4: Expansions (Including Substitution)

Exercise 4(A)Exercise 4(B)Exercise 4(C)Exercise 4(D)Exercise 4(E)
Selina Concise Class 9 Mathematics - Shaalaa.com

Selina solutions for Class 9 Mathmetics chapter 4 - Expansions (Including Substitution)

Selina solutions for Class 9 chapter 4 (Expansions (Including Substitution)) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Selina Concise Class 9 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Selina textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 9 Mathmetics chapter 4 Expansions (Including Substitution) are Algebraic Identities, Expansion of ( a + b )3, Expansion of Formula, Special Product, Method of Cross - Multiplication.

Using Selina Class 9 solutions Expansions (Including Substitution) exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 9 prefer Selina Textbook Solutions to score more in exam.

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