We Distribute, Yet Things Multiply Worksheet and Video Notes on Distribution Properties & Identities

Class 8 Maths Worksheet – We Distribute, Yet Things Multiply

Ganita Prakash | Chapter 6 | Exam Preparation Worksheet

This worksheet covers the Distributive Property, Algebraic Identities, Expansion, Simplification and Fast Multiplication from Chapter 6 “We Distribute, Yet Things Multiply.”

Section A – Distributive Property

1. Use the Distributive Property to find:

1. 24 × 7
2. 36 × 12
3. 48 × 15
4. 125 × 32

2. Rewrite each expression using the Distributive Property.

1. 17 × 98
2. 25 × 49
3. 32 × 101
4. 45 × 99

3. Simplify using the Distributive Property:

1. 7(x + 5)
2. 9(a + 4)
3. 6(p − 3)
4. 12(2x + 5)

📐 Section B – Identity 1A

Identity 1A:
(a + b)² = a² + 2ab + b²

4. Expand using Identity 1A:

1. (x + 5)²
2. (a + 7)²
3. (2x + 3)²
4. (3p + 4)²

5. Find the value using Identity 1A:

1. 25²
2. 102²
3. 49²
4. 103²

6. If x + 1/x = 5, find x² + 1/x².

📐 Section C – Identity 1B

Identity 1B:
(a − b)² = a² − 2ab + b²

7. Expand using Identity 1B:

1. (x − 4)²
2. (a − 6)²
3. (2x − 5)²
4. (3p − 2)²

8. Find the value using Identity 1B:

1. 98²
2. 97²
3. 48²
4. 999²

9. If x − 1/x = 3, find x² + 1/x².

📐 Section D – Identity 1C

Identity 1C:
(a + b)(a − b) = a² − b²

10. Simplify using Identity 1C:

1. (x + 5)(x − 5)
2. (a + 8)(a − 8)
3. (2x + 3)(2x − 3)
4. (5p + 4)(5p − 4)

11. Calculate using Identity 1C:

1. 98 × 102
2. 45 × 55
3. 97 × 103
4. 996 × 1004

12. Find the value of:

1. 51² − 49²
2. 102² − 98²

📐 Section E – Product of Two Binomials

Identity:
(a + m)(b + n) = ab + mb + an + mn

13. Expand using the identity:

1. (x + 2)(y + 3)
2. (a + 4)(b + 5)
3. (p + 3)(q − 2)
4. (2x + 3)(x + 5)

14. Expand and simplify:

1. (x + 7)(x + 2)
2. (x − 3)(x + 5)
3. (2a + 1)(3a + 4)
4. (3p − 2)(2p + 5)

⚡ Section F – Fast Multiplication Using the Distributive Property

15. Calculate using the Distributive Property:

1. 3874 × 11
2. 5678 × 11
3. 2456 × 101
4. 832 × 1001

16. Calculate mentally using a suitable distributive form:

1. 89 × 101
2. 949 × 101
3. 265831 × 1001
4. 1111 × 1001

17. Use the Distributive Property to calculate:

1. 9734 × 99
2. 23478 × 999
3. 567 × 999
4. 428 × 99

Section G – Mixed Exam Practice

18. Choose the correct identity for each expression:

1. (x + 7)²
2. (x − 9)²
3. (x + 5)(x − 5)
4. (a + m)(b + n)

19. Fill in the blanks:

1. (a + b)² = a² + ______ + b²
2. (a − b)² = a² − ______ + b²
3. (a + b)(a − b) = ______ − b²
4. a(b + c) = ______ + ______

20. Expand and simplify:

1. (x + 6)²
2. (2x − 7)²
3. (3a + 2)(3a − 2)
4. (x + 4)(x + 9)

21. Find the value without using long multiplication:

1. 99²
2. 101²
3. 48 × 52
4. 997 × 1003

22. If x + 1/x = 6, find:

1. x² + 1/x²

23. If x − 1/x = 5, find:

1. x² + 1/x²

24. Simplify using suitable identities:

1. (x + 10)² − x²
2. (x + 6)(x − 6)
3. (x + 3)² − 6x
4. (x − 5)² + 10x

25. Challenge Question ⭐

If x + 1/x = 4, find the value of

x² + 1/x².

🎯 Exam Challenge

26. Without directly multiplying, find:

1. 999 × 1001
2. 1002 × 998
3. 49 × 51
4. 9998 × 10002

27. Simplify:

(x + 5)² − (x − 5)²

28. Using an appropriate identity, find the value of:

103² − 97²

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📚 Topics Covered

• Distributive Property
• Identity 1A – (a + b)²
• Identity 1B – (a − b)²
• Identity 1C – (a + b)(a − b)
• (a + m)(b + n) Identity
• Expansion and Simplification
• Fast Multiplication using ×11, ×101 and ×1001
• Fast Multiplication using ×99 and ×999
• Identity-based Exam Questions

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