Chapters
Chapter 2: Exponents
Chapter 3: Squares and Square Root
Chapter 4: Cubes and Cube Roots
Chapter 5: Playing with Numbers
Chapter 6: Sets
Chapter 7: Percent and Percentage
Chapter 8: Profit, Loss and Discount
Chapter 9: Interest
Chapter 10: Direct and Inverse Variations
Chapter 11: Algebraic Expressions
Chapter 12: Identities
Chapter 13: Factorisation
Chapter 14: Linear Equations in one Variable
Chapter 15: Linear Inequations
Chapter 16: Understanding Shapes
Chapter 17: Special Types of Quadrilaterals
Chapter 18: Constructions
Chapter 19: Representing 3-D in 2-D
Chapter 20: Area of a Trapezium and a Polygon
Chapter 21: Surface Area, Volume and Capacity
Chapter 22: Data Handling
Chapter 23: Probability

Chapter 12: Identities
Selina solutions for Concise Mathematics Class 8 ICSE Chapter 12 Identities Exercise 12 (A) [Page 150]
Use direct method to evaluate the following products :
(x + 8)(x + 3)
Use the direct method to evaluate the following products :
(y + 5)(y – 3)
Use the direct method to evaluate the following products :
(a – 8) (a + 2)
Use the direct method to evaluate the following products :
(b – 3) (b – 5)
Use the direct method to evaluate the following products :
(3x – 2y) (2x + y)
Use the direct method to evaluate the following products :
(5a + 16) (3a – 7)
Use the direct method to evaluate the following products :
(8 – b) (3 + b)
Use the direct method to evaluate :
(x+1) (x−1)
Use the direct method to evaluate :
(2+a) (2−a)
Use the direct method to evaluate :
(3b−1) (3b+1)
Use the direct method to evaluate :
(4+5x) (4−5x)
Use the direct method to evaluate :
(2a+3) (2a−3)
Use the direct method to evaluate :
(xy+4) (xy−4)
Use the direct method to evaluate :
(ab+x2) (ab−x2)
Use the direct method to evaluate :
(3x2+5y2) (3x2−5y2)
Use the direct method to evaluate :
`("z"-2/3)("z"+2/3)`
Use the direct method to evaluate :
`(3/5"a"+1/2)(3/5"a"-1/2)`
Use the direct method to evaluate :
(0.5a−2a) (0.5+2a)
Use the direct method to evaluate :
`("a"/2-"b"/3)("a"/2+"b"/3)`
Evaluate : (a+1) (a-1) (a2+1)
Evaluate : (a+b) (a−b) (a2+b2)
Evaluate : (2a−b) (2a+b) (4a2+b2)
Evaluate : (3−2x) (3+2x) (9+4x2)
Evaluate : (3x−4y) (3x+4y) (9x2+16y2)
Use the product (a + b) (a – b) = a2 – b2 to evaluate:
21 x 19
Use the product (a + b) (a – b) = a2 – b2 to evaluate:
33 x 27
Use the product (a + b) (a – b) = a2 – b2 to evaluate:
103 x 97
Use the product (a + b) (a – b) = a2 – b2 to evaluate:
9.8 x 10.2
Use the product (a + b) (a – b) = a2 – b2 to evaluate:
7.7 x 8.3
Use the product (a + b) (a – b) = a2 – b2 to evaluate:
4.6 x 5.4
Evaluate : (6 – xy) (6 + xy)
Evaluate : `(7"x"+2/3"y")(7"x"-2/3"y")`
Evaluate : `("a"/(2"b")+(2"b")/"a")("a"/(2"b")-(2"b")/"a")`
Evaluate : `(3"x"-1/(2"y"))(3"x"+1/(2"y"))`
Evaluate : (2a +3) (2a − 3) (4a2 + 9)
Evaluate : (a + bc) (a − bc) (a2 + b2c2)
Evaluate : (5x + 8y) (3x + 5y)
Evaluate : (7x + 15y) (5x − 4y)
Evaluate : (2a − 3b) (3a + 4b)
Evaluate : (9a − 7b) (3a − b)
Selina solutions for Concise Mathematics Class 8 ICSE Chapter 12 Identities Exercise 12 (B) [Page 152]
Expand : (2a + b)2
Expand : (a – 2b)2
Expand : `("a"+1/(2"a"))^2`
Expand : `(2"a"-1/"a")^2`
Expand : (a+b−c)2
Expand : (a−b+c)2
Expand : `(3"x"+1/(3"x"))^2`
Expand : `(2"x"-1/(2"x"))^2`
Find the square of x+ 3y
Find the square of 2x − 5y
Find the square of `"a"+1/(5"a")`
Find the square of `2"a"-1/"a"`
Find the square of x − 2y +1
Find the square of 3a − 2b − 5c
Find the square of `2"x"+1/"x"+1`
Find the square of `5-"x"+2/"x"`
Find the square of 2x − 3y + z
Find the square of `"x"+1/"x"-1`
Evaluate using the expansion of (a + b)2 or (a – b)2 :
(208)2
Evaluate using the expansion of (a + b)2 or (a – b)2 :
(92)2
Evaluate using the expansion of (a + b)2 or (a – b)2 :
(415)2
Evaluate using the expansion of (a + b)2 or (a – b)2 :
(188)2
Evaluate using the expansion of (a + b)2 or (a – b)2 :
(9.4)2
Evaluate using the expansion of (a + b)2 or (a – b)2 :
(20.7)2
Expand : (2a + b)3
Expand : (a − 2b)3
Expand : (3x − 2y)3
Expand : (x + 5y)3
Expand : `("a"+1/"a")^3`
Expand : `(2"a"-1/(2"a"))^3`
Find the cube of: a + 2
Find the cube of: 2a − 1
Find the cube of: 2a + 3b
Find the cube of: 3b − 2a
Find the cube of: `2"x"+1/"x"`
Find the cube of: `"x"-1/2`
Selina solutions for Concise Mathematics Class 8 ICSE Chapter 12 Identities Exercise 12 (C) [Pages 154 - 155]
If a+b=5 and ab = 6, find a2 + b2
If a – b = 6 and ab = 16, find a2 + b2
If a2 + b2 = 29 and ab = 10, find : a + b
If a2 + b2 = 29 and ab = 10, find : a − b
If a2 + b2= 10 and ab = 3; find : a – b
If a2 + b2= 10 and ab = 3; find : a + b
If `"a" + 1/"a"=3`, find `"a"^2+1/"a"^2`
If `"a" - 1/"a"=4`, find : `"a"^2+1/"a"^2`
If `"a"^2+ 1/"a"^2=23`, find : `"a" +1/"a"`
If `"a"^2+ 1/"a"^2=11`, find : `"a" -1/"a"`
If a + b + c = 10 and a2 + b2 + c2 = 38, find : ab + bc + ca
Find : a2 + b2 + c2, if a + b + c = 9 and ab + bc + ca = 24
Find : a + b + c, if a2 + b2 + c2 = 83 and ab + bc + ca = 71.
If a + b = 6 and ab=8, find : a3 + b3.
If a – b = 3 and ab = 10, find : a3 – b3.
Find : `"a"^3+1/"a"^3`, if `"a" +1/"a"=5`.
Find : `"a"^3-1/"a"^3`, if `"a" -1/"a"=4`.
If `2"x"-1/(2"x")=4`, find : `4"x"^2+1/(4"x"^2)`
If `2"x"-1/(2"x")=4`, find : `8"x"^3-1/(8"x"^3)`
If `3"x"+1/(3"x")=3`, find : `9"x"^2+1/(9"x"^2)`
If `3"x"+1/(3"x")=3`, find : `27"x"^3+1/(27"x"^3)`
The sum of the squares of two numbers is 13 and their product is 6. Find:
(i) the sum of the two numbers.
(ii) the difference between them.
Selina solutions for Concise Mathematics Class 8 ICSE Chapter 12 Identities Exercise 12 (D) [Page 155]
Evaluate: `(3"x"+1/2)(2"x"+1/3)`
Evaluate: (2a + 0.5) (7a − 0.3)
Evaluate: (9 − y) (7 + y)
Evaluate: (2 − z) (15 − z)
Evaluate: (a2 + 5) (a2 − 3)
Evaluate: (4 − ab) (8 + ab)
Evaluate: (5xy − 7) (7xy + 9)
Evaluate: (3a2 − 4b2) (8a2 − 3b2)
Evaluate: `(2"x"-3/5)(2"x"+3/5)`
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Evaluate: (6 − 5xy) (6 + 5xy)
Evaluate: `(2"a"+1/"2a")(2"a"-1/"2a")`
Evaluate: (4x2 − 5y2) (4x2 + 5y2)
Evaluate: (1.6x + 0.7y) (1.6x − 0.7y)
Evaluate: (m + 3) (m − 3) (m2 + 9)
Evaluate: (3x + 4y) (3x − 4y) (9x2 + 16y2)
Evaluate: (a + bc) (a − bc) (a2 + b2c2)
Evaluate: 203 × 197
Evaluate: 20.8 × 19.2
Find the square of `3"x"+2/"y"`
Find the square of `"5a"/"6b"-"6b"/"5a"`
Find the square of `2"m"^2-2/3"n"^2`
Find the square of `5"x"+1/(5"x")`
Find the square of `8"x"+3/2"y"`
Find the square of 607
Find the square of 391
Find the square of 9.7
If `"a" +1/"a"=2`, find : `"a"^2+1/"a"^2`
If `"a" +1/"a"=2`, find : `"a"^4+1/"a"^4`
If `"m" -1/"m"=5`, find : `"m"^2+1/"m"^2`
If `"m" -1/"m"=5`, find : `"m"^4+1/"m"^4`
If `"m" -1/"m"=5`, find : `"m"^2-1/"m"^2`
If a2 + b2 = 41 and ab = 4, find : a – b
If a2 + b2 = 41 and ab = 4, find : a + b
If `2"a"+1/(2"a")=8`, find : `4"a"^2+1/(4"a"^2)`
If `2"a"+1/(2"a")=8`, find : `16"a"^4+1/(16"a"^4)`
If `3"x"-1/(3"x")=5`, find : `9"x"^2+1/(9"x"^2)`
If `3"x"-1/(3"x")=5`, find : `81"x"^4+1/(81"x"^4)`
Expand : (3x – 4y + 5z)2
Expand : (2a – 5b – 4c)2
Expand : (5x + 3y)3
Expand : (6a – 7b)3
If a + b + c = 9 and ab + bc + ca = 15, find: a2 + b2 + c2.
If a + b + c = 11 and a2 + b2 + c2 = 81, find : ab + bc + ca.
If 3x – 4y = 5 and xy = 3, find : 27x3 – 64y3.
If a + b = 8 and ab = 15, find : a3 + b3.
If 3x + 2y = 9 and xy = 3, find : 27x3 + 8y3.
If 5x – 4y = 7 and xy = 8, find : 125x3 – 64y3.
The difference between the two numbers is 5 and their products are 14. Find the difference between their cubes.
Chapter 12: Identities

Selina solutions for Concise Mathematics Class 8 ICSE chapter 12 - Identities
Selina solutions for Concise Mathematics Class 8 ICSE chapter 12 (Identities) 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 Concise Mathematics Class 8 ICSE solutions in a manner that help students grasp basic concepts better and faster.
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Concepts covered in Concise Mathematics Class 8 ICSE chapter 12 Identities are Algebraic Identities, Product of Sum and Difference of Two Terms, Important Formula of Expansion, Cubes of Binomials, Application of Formulae, Expansion Form of Numbers.
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