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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-17-CON-01
Conditional Identities - Assignment
Chapter: Expansions
Topic: Conditional Identities and Substitutions
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.
If $a+b+c=0$, then $a^3+b^3+c^3=$
  • A.$0$
  • B.$abc$
  • C.$3abc$
  • D.$a^3b^3c^3$
2.
$a^3-b^3-3abc$ relates to the identity for:
  • A.$a^2-b^2$
  • B.$a^3+b^3+c^3-3abc$
  • C.$(a+b)^2$
  • D.$(a-b)^2$
3.
$a^3+b^3=$
  • 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.$(a+b)^3$
4.
$a^3-b^3=$
  • 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.$(a-b)^3$
5.
If $a+b+c=0$ and $abc=4$, then $a^3+b^3+c^3=$
  • A.$4$
  • B.$8$
  • C.$12$
  • D.$0$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $a+b+c=0$, write $a^3+b^3+c^3$.
7.
Factorise $a^3+b^3$.
8.
Factorise $a^3-b^3$.
9.
If $a+b+c=0$ and $abc=2$, find $a^3+b^3+c^3$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Evaluate $1^3+2^3+(-3)^3$ using the identity (since $1+2-3=0$).
11.
If $a+b+c=0$ and $ab+bc+ca=-5$, find $a^2+b^2+c^2$.
12.
Factorise $8a^3+27b^3$.
13.
Factorise $27x^3-1$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Using $x+y+z=0\Rightarrow x^3+y^3+z^3=3xyz$, evaluate $25^3+(-13)^3+(-12)^3$.
15.
Show that if $x+y+z=0$ then $x^3+y^3+z^3=3xyz$, and use it to evaluate $7^3+(-3)^3+(-4)^3$.

Answer Key

Section A — Multiple Choice Questions
  1. (C) $3abc$
  2. (B) $a^3+b^3+c^3-3abc$
  3. (A) $(a+b)(a^2-ab+b^2)$
  4. (B) $(a-b)(a^2+ab+b^2)$
  5. (C) $12$
Section B — Short Answer (2 marks)
  1. $3abc$.
  2. $(a+b)(a^2-ab+b^2)$.
  3. $(a-b)(a^2+ab+b^2)$.
  4. $6$.
Section C — Short Answer (3 marks)
  1. $-18$.
  2. $10$.
  3. $(2a+3b)(4a^2-6ab+9b^2)$.
  4. $(3x-1)(9x^2+3x+1)$.
Section D — Long Answer (5 marks)
  1. $11700$.
  2. $252$.
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