Math Homework Pack (Print-Friendly)
Topic A: Algebraic Identities (Laws 1–9) | Topic B: Decimal Division
Student: Rayyan School: Playpen
Date: 07 January 2026
Copy: Student
Topic A — Algebraic Identities (Laws 1–9)
Instructions: Use the laws. Show working neatly.
1. (a + b)2 = a2 + 2ab + b2
6. (a + b)2 - (a - b)2 = 4ab
2. (a - b)2 = a2 - 2ab + b2
7. (a - b)2 = (a + b)2 - 4ab
3. a2 - b2 = (a + b)(a - b)
8. (a + b)2 = (a - b)2 + 4ab
4. a2 + b2 = (a + b)2 - 2ab
9. 2(a2 + b2) = (a + b)2 + (a - b)2
5. a2 + b2 = (a - b)2 + 2ab
Questions (A1–A25)
A1.
Expand: (x + 7)2
A2.
Expand: (12 + y)2
A3.
Expand: (a + 9)2
A4.
Expand: (5m + 2)2
A5.
Expand: (p + 3q)2
A6.
Expand: (x - 6)2
A7.
Expand: (15 - y)2
A8.
Expand: (a - 4b)2
A9.
Expand: (9m - 1)2
A1
0.
Expand: (2p - 5)2
A1
1.
Factorise: x2 - 49
A1
2.
Factorise: 81 - y2
A1
3.
Factorise: 25a2 - 16
A1
4.
Factorise: (3m)2 - (2n)2
A1
5.
Factorise: p2 - 36q2
A1
6.
Find: a2 + b2 if (a + b)2 = 169 and ab = 30
A1
7.
Find: a2 + b2 if (a - b)2 = 81 and ab = 18
A1
8.
Find: a2 + b2 if (a + b)2 = 196 and ab = 40
A1
9.
Find: (a + b)2 - (a - b)2 if a = 9, b = 2
A2
0.
Find: (a - b)2 if (a + b)2 = 144 and ab = 20
A2
1.
Find: (a + b)2 if (a - b)2 = 121 and ab = 24
A2
2.
Find: a2 + b2 if (a + b) = 15 and (a - b) = 5
A2
3.
Find: a2 + b2 if (a + b) = 18 and (a - b) = 6
A2
4.
Compute: Let a = 5 and b = 3. Find (a + b)2
and (a - b)2
A2
5.
Compute: Let a = 7 and b = 4. Find a2 - b2
Topic B — Decimal Division (Easy → Hard)
Tip: If the divisor is a decimal, multiply both numbers by 10, 100, etc. to make it a whole number.
Questions (B1–B15)
B1.
Calculate: 4.8 ÷ 2
B2.
Calculate: 7.5 ÷ 3
B3.
Calculate: 12.6 ÷ 6
B4.
Calculate: 9.24 ÷ 4
B5.
Calculate: 15.75 ÷ 5
B6.
Calculate: 0.84 ÷ 7
B7.
Calculate: 6.3 ÷ 9
B8.
Calculate: 18.36 ÷ 12
B9.
Calculate: 3.6 ÷ 0.3
B1
0.
Calculate: 8.4 ÷ 0.7
B1
1.
Calculate: 5.04 ÷ 0.6
B1
2.
Calculate: 2.5 ÷ 0.05
B1
3.
Calculate: 0.72 ÷ 0.8
B1
4.
Calculate: 16.2 ÷ 0.9
B1
5.
Calculate: 45.6 ÷ 1.2
Write final answers clearly. Include working for full marks.