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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-17-SUM-01
Expansions of (a +/- b) - Assignment
Chapter: Expansions
Topic: Expansions of (a +/- b)
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.
$(a+b)^2=$
  • A.$a^2+b^2$
  • B.$a^2+2ab+b^2$
  • C.$a^2-2ab+b^2$
  • D.$2ab$
2.
$(a-b)^2=$
  • A.$a^2-b^2$
  • B.$a^2-2ab+b^2$
  • C.$a^2+2ab+b^2$
  • D.$a^2-ab$
3.
$(a+b)(a-b)=$
  • A.$a^2+b^2$
  • B.$a^2-b^2$
  • C.$2ab$
  • D.$a^2$
4.
$(x+5)^2=$
  • A.$x^2+25$
  • B.$x^2+10x+25$
  • C.$x^2+5x+25$
  • D.$x^2+25x$
5.
$(x-2)^2=$
  • A.$x^2-4$
  • B.$x^2-4x+4$
  • C.$x^2+4x+4$
  • D.$x^2-2x+4$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Expand $(x+4)^2$.
7.
Expand $(x-3)^2$.
8.
Expand $(2x+1)^2$.
9.
Expand $(x+7)(x-7)$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Expand $(3x+2)^2$.
11.
Expand $(2a-5)^2$.
12.
Find $\left(x+\tfrac1x\right)^2$.
13.
Expand $(5x+3)(5x-3)$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
If $x+\tfrac1x=5$, find $x^2+\tfrac{1}{x^2}$.
15.
Expand $(2x+3y)^2$ and $(2x-3y)^2$ and add them.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $a^2+2ab+b^2$
  2. (B) $a^2-2ab+b^2$
  3. (B) $a^2-b^2$
  4. (B) $x^2+10x+25$
  5. (B) $x^2-4x+4$
Section B — Short Answer (2 marks)
  1. $x^2+8x+16$.
  2. $x^2-6x+9$.
  3. $4x^2+4x+1$.
  4. $x^2-49$.
Section C — Short Answer (3 marks)
  1. $9x^2+12x+4$.
  2. $4a^2-20a+25$.
  3. $x^2+2+\tfrac{1}{x^2}$.
  4. $25x^2-9$.
Section D — Long Answer (5 marks)
  1. $23$.
  2. $8x^2+18y^2$.
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