AmbifulWorksheets
Practice that never repeats
CBSE · Class 8 · Mathematics

We Distribute, Yet Things Multiply

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
Using (a + b)2, 622 equals:
  1. 3845
  2. 3604
  3. 3724
  4. 3844
2.
Using (a − b)2, 862 equals:
  1. 7756
  2. 7404
  3. 7396
  4. 8084
3.
(a + b)2 equals:
  1. a2 + ab + b2
  2. 2a + 2b
  3. a2 + b2
  4. a2 + 2ab + b2
4.
872 − 112 equals:
  1. 7448
  2. 5776
  3. 152
  4. 7449
5.
(x − 4)(x − 5) equals:
  1. x2 − 9x − 9
  2. x2 − 9x + 20
  3. x2 + 20x − 9
  4. x2 + 20
6.
72 × 68 equals:
  1. 4896
  2. 4898
  3. 4900
  4. 4904
7.
Using (a + b)2, 212 equals:
  1. 441
  2. 442
  3. 421
  4. 401
8.
(2x + 6)2 equals:
  1. 4x2 + 24x + 36
  2. 4x2 + 12x + 36
  3. 4x2 + 36
  4. 2x2 + 24x + 36
Section B — Short answer8 × 2 = 16 marks
9.
Expand (x + 3)(x − 8).
10.
Expand (6y − 9)2.
11.
Find 107 × 93 using an identity.
12.
If a + b = 34 and ab = 288, find a2 + b2.
13.
Expand (5m − 6n)2.
14.
A rectangle is (x + 6) cm by (x + 8) cm. Write its area as an expression, then find it when x = 12.
15.
Simplify (x + 9)2 − (x − 9)2, and check your answer for x = 18.
16.
Multiply 6x(2x + 10).
Section C — Word problems4 × 4 = 16 marks
17.
A square garden of side 24 m has a path 2 m wide all round its outside. Find the area of the path.
18.
Rahul buys 101 books at Rs 99 each. Use an identity to find the total quickly.
19.
A square tile of side 53 cm has a square hole of side 47 cm cut out. What area is left?
20.
A rectangle 13 m by 11 m has both its length and breadth increased by 4 m. By how much does its area increase?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 8 · Mathematics

Answer key

We Distribute, Yet Things Multiply · AW-8M-IDN-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 3844602 + 2 × 60 × 2 + 22 = 3600 + 240 + 4
2(c) 7396902 − 2 × 90 × 4 + 42 = 8100 − 720 + 16
3(d) a2 + 2ab + b2—
4(a) 7448(87 + 11)(87 − 11) = 98 × 76
5(b) x2 − 9x + 20x2 + (−4 + (−5))x + (−4 × (−5))
6(a) 4896702 − 22 = 4900 − 4
7(a) 441400 + 40 + 1
8(a) 4x2 + 24x + 36(2x)2 + 2 × 2x × 6 + 62
9x2 − 5x − 24x2 − 8x + 3x − 24
1036y2 − 108y + 81(6y)2 − 2 × 6y × 9 + 92
119951(a + b)(a − b) = a2 − b2: 10000 − 49
12580(a + b)2 − 2ab = 1156 − 576
1325m2 − 60mn + 36n2(5m)2 − 2 × 5m × 6n + (6n)2
14x2 + 14x + 48; 360 cm218 × 20 = 360
1536x; 648729 − 81 = 648
1612x2 + 60x6x × 2x + 6x × 10
17208 m2282 − 242 = (28 + 24)(4) = 208
18Rs 9,999101 × 99 = 1002 − 12 = 9999
19600 cm2532 − 472 = (53 + 47)(53 − 47) = 100 × 6
20112 m2(13 + 4)(11 + 4) − 13 × 11 = 4(13 + 11) + 42