Vidaara.orgClass 9 · Mathematics
CodeVID-M09-02-FAC-01
Factorization Using Identities — 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.
$a^2-b^2=$
- A.$(a+b)(a-b)$
- B.$(a-b)^2$
- C.$(a+b)^2$
- D.$a^2+b^2$
2.
$a^2+2ab+b^2=$
- A.$(a-b)^2$
- B.$(a+b)^2$
- C.$(a+b)(a-b)$
- D.$2ab$
3.
$a^3+b^3=$
- A.$(a+b)(a^2-ab+b^2)$
- B.$(a+b)^3$
- C.$(a-b)(a^2+ab+b^2)$
- D.$(a+b)(a-b)$
4.
$x^2+5x+6=$
- A.$(x+2)(x+3)$
- B.$(x-2)(x-3)$
- C.$(x+1)(x+6)$
- D.$(x+6)(x-1)$
5.
$a^3-b^3=$
- A.$(a-b)(a^2+ab+b^2)$
- B.$(a+b)(a^2-ab+b^2)$
- C.$(a-b)^3$
- D.$(a-b)(a+b)$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Factorise $x^2-9$.
7.
Factorise $x^2+6x+9$.
8.
Factorise $x^2-7x+12$.
9.
Factorise $a^3+27$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Factorise $4x^2-25$.
11.
Factorise $x^2+8x+16$.
12.
Factorise $8x^3-27$.
13.
Factorise $x^2-x-12$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Factorise $x^3+3x^2-4x-12$ by grouping.
15.
Factorise $27x^3+8$ and $64-y^3$.
Answer Key
Section A — Multiple Choice Questions
- (A) $(a+b)(a-b)$
- (B) $(a+b)^2$
- (A) $(a+b)(a^2-ab+b^2)$
- (A) $(x+2)(x+3)$
- (A) $(a-b)(a^2+ab+b^2)$
Section B — Short Answer (2 marks)
- $(x+3)(x-3)$.
- $(x+3)^2$.
- $(x-3)(x-4)$.
- $(a+3)(a^2-3a+9)$.
Section C — Short Answer (3 marks)
- $(2x+5)(2x-5)$.
- $(x+4)^2$.
- $(2x-3)(4x^2+6x+9)$.
- $(x-4)(x+3)$.
Section D — Long Answer (5 marks)
- $(x+3)(x-2)(x+2)$.
- $(3x+2)(9x^2-6x+4)$ and $(4-y)(16+4y+y^2)$.
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