← Back to topic
Vidaara.orgClass 9 · Mathematics
CodeVID-M09-18-CUB-01
Sum & Difference of Cubes - Assignment
Chapter: Factorisation
Topic: Sum and Difference of Cubes
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
$a^3+b^3=$
  • A.$(a+b)(a^2-ab+b^2)$
  • B.$(a+b)(a^2+ab+b^2)$
  • C.$(a-b)(a^2+ab+b^2)$
  • D.$(a+b)^3$
2.
$a^3-b^3=$
  • A.$(a-b)(a^2+ab+b^2)$
  • B.$(a-b)(a^2-ab+b^2)$
  • C.$(a+b)(a^2-ab+b^2)$
  • D.$(a-b)^3$
3.
$x^3+8=$
  • A.$(x+2)(x^2-2x+4)$
  • B.$(x+2)(x^2+2x+4)$
  • C.$(x-2)(x^2+2x+4)$
  • D.$(x+2)^3$
4.
$x^3-27=$
  • A.$(x-3)(x^2+3x+9)$
  • B.$(x-3)(x^2-3x+9)$
  • C.$(x+3)(x^2-3x+9)$
  • D.$(x-3)^3$
5.
In $x^3+8$, the value of $b$ is:
  • A.$2$
  • B.$3$
  • C.$4$
  • D.$8$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Factorise $x^3+1$.
7.
Factorise $x^3-1$.
8.
Factorise $x^3+27$.
9.
Factorise $x^3-8$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Factorise $8x^3+27$.
11.
Factorise $27x^3-64$.
12.
Factorise $125x^3+1$.
13.
Factorise $x^3-125$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Factorise $64a^3-27b^3$.
15.
Factorise $8x^3+125y^3$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $(a+b)(a^2-ab+b^2)$
  2. (A) $(a-b)(a^2+ab+b^2)$
  3. (A) $(x+2)(x^2-2x+4)$
  4. (A) $(x-3)(x^2+3x+9)$
  5. (A) $2$
Section B — Short Answer (2 marks)
  1. $(x+1)(x^2-x+1)$.
  2. $(x-1)(x^2+x+1)$.
  3. $(x+3)(x^2-3x+9)$.
  4. $(x-2)(x^2+2x+4)$.
Section C — Short Answer (3 marks)
  1. $(2x+3)(4x^2-6x+9)$.
  2. $(3x-4)(9x^2+12x+16)$.
  3. $(5x+1)(25x^2-5x+1)$.
  4. $(x-5)(x^2+5x+25)$.
Section D — Long Answer (5 marks)
  1. $(4a-3b)(16a^2+12ab+9b^2)$.
  2. $(2x+5y)(4x^2-10xy+25y^2)$.
Generated by Vidaara.org · Assignment VID-M09-18-CUB-01 · vidaara.org