Chapters
Chapter 2: Profit , Loss and Discount
Chapter 3: Compound Interest
Chapter 4: Expansions
Chapter 5: Factorisation
Chapter 6: Changing the subject of a formula
Chapter 7: Linear Equations
Chapter 8: Simultaneous Linear Equations
Chapter 9: Indices
Chapter 10: Logarithms
Chapter 11: Triangles and their congruency
Chapter 12: Isosceles Triangle
Chapter 13: Inequalities in Triangles
Chapter 14: Constructions of Triangles
Chapter 15: Mid-point and Intercept Theorems
Chapter 16: Similarity
Chapter 17: Pythagoras Theorem
Chapter 18: Rectilinear Figures
Chapter 19: Quadrilaterals
Chapter 20: Constructions of Quadrilaterals
Chapter 21: Areas Theorems on Parallelograms
Chapter 22: Statistics
Chapter 23: Graphical Representation of Statistical Data
Chapter 24: Perimeter and Area
Chapter 25: Surface Areas and Volume of Solids
Chapter 26: Trigonometrical Ratios
Chapter 27: Trigonometrical Ratios of Standard Angles
Chapter 28: Coordinate Geometry
Chapter 4: Expansions
Frank solutions for Class 9 Maths ICSE Chapter 4 Expansions Exercise 4.1
Expand the following:
(a + 4) (a + 7)
Expand the following:
(m + 8) (m - 7)
Expand the following:
(x - 5) (x - 4)
Expand the following:
(3x + 4) (2x - 1)
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
Expand the following:
(a + 3b)2
Expand the following:
(2p - 3q)2
Expand the following:
`(2"a" + 1/(2"a"))^2`
Expand the following:
(x - 3y - 2z)2
Find the squares of the following:
9m - 2n
Find the squares of the following:
3p - 4q2
Find the squares of the following:
`(7x)/(9y) - (9y)/(7x)`
Find the squares of the following:
(2a + 3b - 4c)
Simplify by using formula :
(5x - 9) (5x + 9)
Simplify by using formula :
(2x + 3y) (2x - 3y)
Simplify by using formula :
(a + b - c) (a - b + c)
Simplify by using formula :
(x + y - 3) (x + y + 3)
Simplify by using formula :
(1 + a) (1 - a) (1 + a2)
Simplify by using formula :
`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`
Evaluate the following without multiplying:
(95)2
Evaluate the following without multiplying:
(103)2
Evaluate the following without multiplying:
(999)2
Evaluate the following without multiplying:
(1005)2
Evaluate, using (a + b)(a - b)= a2 - b2.
399 x 401
Evaluate, using (a + b)(a - b)= a2 - b2.
999 x 1001
Evaluate, using (a + b)(a - b)= a2 - b2.
4.9 x 5.1
Evaluate, using (a + b)(a - b)= a2 - b2.
15.9 x 16.1
If a - b = 10 and ab = 11; find a + b.
If x + y = 9, xy = 20
find: x - y
If x + y = 9, xy = 20
find: x2 - y2.
If `"a" + 1/"a" = 6;`find `"a" - 1/"a"`
If `"a" + 1/"a" = 6;`find `"a"^2 - 1/"a"^2`
If `"a" - 1/"a" = 10;` find `"a" + 1/"a"`
If `"a" - 1/"a" = 10`; find `"a"^2 - 1/"a"^2`
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
If `x + (1)/x = 3`; find `x^4 + (1)/x^4`
If p + q = 8 and p - q = 4, find:
pq
If p + q = 8 and p - q = 4, find:
p2 + q2
If m - n = 0.9 and mn = 0.36, find:
m + n
If m - n = 0.9 and mn = 0.36, find:
m2 - n2.
If x + y = 1 and xy = -12; find:
x - y
If x + y = 1 and xy = -12; find:
x2 - y2.
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a" + (1)/"a"`
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a"^2 + (1)/"a"^2`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" - (1)/"a"`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a"^2 - (1)/"a"^2`
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.
If a2 + b2 + c2 = 41 and a + b + c = 9; find ab + bc + ca.
If p2 + q2 + r2 = 82 and pq + qr + pr = 18; find p + q + r.
If x + y + z = p and xy + yz + zx = q; find x2 + y2 + z2.
Frank solutions for Class 9 Maths ICSE Chapter 4 Expansions Exercise 4.2
Find the cube of: 2a - 5b
Find the cube of: 4x + 7y
Find the cube of: `3"a" + (1)/(3"a")`
Find the cube of: `4"p" - (1)/"p"`
Find the cube of: `(2"m")/(3"n") + (3"n")/(2"m")`
Find the cube of: `"a" - (1)/"a" + "b"`
If `5x + (1)/(5x) = 7`; find the value of `125x^3 + (1)/(125x^3)`.
If `3x - (1)/(3x) = 9`; find the value of `27x^3 - (1)/(27x^3)`.
If `x + (1)/x = 5`, find the value of `x^2 + (1)/x^2, x^3 + (1)/x^3` and `x^4 + (1)/x^4`.
If `"a" - (1)/"a" = 7`, find `"a"^2 + (1)/"a"^2 , "a"^2 - (1)/"a"^2` and `"a"^3 - (1)/"a"^3`
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a"^3 + (1)/"a"^3`
If `"m"^2 + (1)/"m"^2 = 51`; find the value of `"m"^3 - (1)/"m"^3`
If `9"a"^2 + (1)/(9"a"^2) = 23`; find the value of `27"a"^3 + (1)/(27"a"^3)`
If `x^2 + (1)/x^2 = 18`; find : `x - (1)/x`
If `x^2 + (1)/x^2 = 18`; find : `x^3 - (1)/x^3`
If `"p" + (1)/"p" = 6`; find : `"p"^2 + (1)/"p"^2`
If `"p" + (1)/"p" = 6`; find : `"p"^4 + (1)/"p"^4`
If `"p" + (1)/"p" = 6`; find : `"p"^3 + (1)/"p"^3`
If `"r" - (1)/"r" = 4`; find: `"r"^2 + (1)/"r"^2`
If `"r" - (1)/"r" = 4`; find : `"r"^4 + (1)/"r"^4`
If `"r" - (1)/"r" = 4`; find : `"r"^3 - (1)/"r"^3`
If `"a" + (1)/"a" = 2`, then show that `"a"^2 + (1)/"a"^2 = "a"^3 + (1)/"a"^3 = "a"^4 + (1)/"a"^4`
If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.
If `"a" + (1)/"a" = "p"`; then show that `"a"^3 + (1)/"a"^3 = "p"("p"^2 - 3)`
If `("a" + 1/"a")^2 = 3`; then show that `"a"^3 + (1)/"a"^3 = 0`
If a + b + c = 0; then show that a3 + b3 + c3 = 3abc.
If a + 2b + c = 0; then show that a3 + 8b3 + c3 = 6abc
If x3 + y3 = 9 and x + y = 3, find xy.
If a + b = 5 and ab = 2, find a3 + b3.
If p - q = -1 and pq = -12, find p3 - q3
If m - n = -2 and m3 - n3 = -26, find mn.
If 2a - 3b = 10 and ab = 16; find the value of 8a3 - 27b3.
If x + 2y = 5, then show that x3 + 8y3 + 30xy = 125.
Simplify:
(4x + 5y)2 + (4x - 5y)2
Simplify:
(7a +5b)2 - (7a - 5b)2
Simplify:
(a + b)3 + (a - b)3
Simplify:
`("a" - 1/"a")^2 + ("a" + 1/"a")^2`
Simplify:
(x + y - z)2 + (x - y + z)2
Simplify:
`("a" + 1/"a")^3 - ("a" - 1/"a")^3`
Simplify:
(2x + y)(4x2 - 2xy + y2)
Simplify:
`(x - 1/x)(x^2 + 1 + 1/x^2)`
Simplify:
(x + 2y + 3z)(x2 + 4y2 + 9z2 - 2xy - 6yz - 3zx)
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
Simplify:
(3a + 2b - c)(9a2 + 4b2 + c2 - 6ab + 2bc +3ca)
Simplify:
(3x + 5y + 2z)(3x - 5y + 2z)
Simplify:
(2x - 4y + 7)(2x + 4y + 7)
Simplify:
(3a - 7b + 3)(3a - 7b + 5)
Evaluate the following :
(3.29)3 + (6.71)3
Evaluate the following :
(5.45)3 + (3.55)3
Evaluate the following :
(8.12)3 - (3.12)3
Evaluate the following :
7.16 x 7.16 + 2.16 x 7.16 + 2.16 x 2.16
Evaluate the following :
1.81 x 1.81 - 1.81 x 2.19 + 2.19 x 2.19
Chapter 4: Expansions
Frank solutions for Class 9 Maths ICSE chapter 4 - Expansions
Frank solutions for Class 9 Maths ICSE chapter 4 (Expansions) 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 Class 9 Maths ICSE 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. Frank 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 Maths ICSE chapter 4 Expansions are Algebraic Identities, Expansion of Formula, Special Product, Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method, Expansion of (a + b)3.
Using Frank Class 9 solutions Expansions 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 Frank Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 9 prefer Frank Textbook Solutions to score more in exam.
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