Vidaara.orgClass 9 · Mathematics
CodeVID-M09-17-TRI-01
Expansion of (a + b + c)^2 - Assignment
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.
$(a+b+c)^2=$
- 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.$(a+b+c)^3$
2.
Number of terms in the expansion of $(a+b+c)^2$:
- A.$3$
- B.$4$
- C.$6$
- D.$9$
3.
$(1+2+3)^2=$
- A.$14$
- B.$36$
- C.$24$
- D.$12$
4.
If $a+b+c=0$, then $a^2+b^2+c^2=$
- A.$0$
- B.$2(ab+bc+ca)$
- C.$-2(ab+bc+ca)$
- D.$abc$
5.
The cross terms of $(a+b+c)^2$ are:
- A.$ab,bc,ca$
- B.$2ab,2bc,2ca$
- C.$a^2,b^2,c^2$
- D.$3ab$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Expand $(x+y+z)^2$.
7.
Find $(a+b+c)^2$ when $a=b=c=1$.
8.
Write the three cross terms of $(a+b+c)^2$.
9.
Evaluate $(2+3+4)^2$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Expand $(x+2y+3z)^2$.
11.
If $a+b+c=6$ and $ab+bc+ca=11$, find $a^2+b^2+c^2$.
12.
Expand $(a-b+c)^2$.
13.
If $a+b+c=0$ and $a^2+b^2+c^2=20$, find $ab+bc+ca$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
If $a+b+c=9$ and $ab+bc+ca=23$, find $a^2+b^2+c^2$.
15.
Expand $(2x-3y+z)^2$.
Answer Key
Section A — Multiple Choice Questions
- (B) $a^2+b^2+c^2+2ab+2bc+2ca$
- (C) $6$
- (B) $36$
- (C) $-2(ab+bc+ca)$
- (B) $2ab,2bc,2ca$
Section B — Short Answer (2 marks)
- $x^2+y^2+z^2+2xy+2yz+2zx$.
- $9$.
- $2ab,\ 2bc,\ 2ca$.
- $81$.
Section C — Short Answer (3 marks)
- $x^2+4y^2+9z^2+4xy+12yz+6zx$.
- $14$.
- $a^2+b^2+c^2-2ab-2bc+2ca$.
- $-10$.
Section D — Long Answer (5 marks)
- $35$.
- $4x^2+9y^2+z^2-12xy-6yz+4zx$.
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