Vidaara.orgClass 9 · Mathematics
CodeVID-M9-17-CT
Expansions — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- 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.
$(a+b+c)^2=$
- A.$a^2+b^2+c^2$
- B.$a^2+b^2+c^2+2ab+2bc+2ca$
- C.$a^2+b^2+c^2+abc$
- D.$(a+b+c)^3$
3.
If $a+b+c=0$, then $a^3+b^3+c^3=$
- A.$0$
- B.$abc$
- C.$3abc$
- D.$a^3b^3c^3$
4.
$(a-b)^2=$
- A.$a^2-b^2$
- B.$a^2-2ab+b^2$
- C.$a^2+2ab+b^2$
- D.$a^2-ab$
5.
Number of terms in the expansion of $(a+b+c)^2$:
- A.$3$
- B.$4$
- C.$6$
- D.$9$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Expand $(x+4)^2$.
7.
Expand $(x+y+z)^2$.
8.
If $a+b+c=0$, write $a^3+b^3+c^3$.
9.
Expand $(x-3)^2$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Expand $(3x+2)^2$.
11.
Expand $(x+2y+3z)^2$.
12.
Evaluate $1^3+2^3+(-3)^3$ using the identity (since $1+2-3=0$).
13.
Expand $(2a-5)^2$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
If $x+\tfrac1x=5$, find $x^2+\tfrac{1}{x^2}$.
15.
If $a+b+c=9$ and $ab+bc+ca=23$, find $a^2+b^2+c^2$.
Answer Key
Section A — Multiple Choice Questions
- (B) $a^2+2ab+b^2$
- (B) $a^2+b^2+c^2+2ab+2bc+2ca$
- (C) $3abc$
- (B) $a^2-2ab+b^2$
- (C) $6$
Section B — Short Answer (2 marks)
- $x^2+8x+16$.
- $x^2+y^2+z^2+2xy+2yz+2zx$.
- $3abc$.
- $x^2-6x+9$.
Section C — Short Answer (3 marks)
- $9x^2+12x+4$.
- $x^2+4y^2+9z^2+4xy+12yz+6zx$.
- $-18$.
- $4a^2-20a+25$.
Section D — Long Answer (5 marks)
- $23$.
- $35$.
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