Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 201 · 40 sums

The method (Split into easy parts): (a + b)² = a² + 2ab + b². (a − b)² = a² − 2ab + b². (a + b)(a − b) = a² − b²; so a² − b² = (a + b)(a − b). a² + b² = (a + b)² − 2ab = (a − b)² + 2ab.

1. 1.Use (a + b)(a − b) = a² − b² to find 22 × 18.
2. 2.Use (a + b)(a − b) = a² − b² to find 61 × 59.
3. 3.Use (a − b)² = a² − 2ab + b² to find 62².
4. 4.Use a² − b² = (a + b)(a − b) to find 78² − 6².
5. 5.Use (a + b)² = a² + 2ab + b² to find 75².
6. 6.Use (a − b)² = a² − 2ab + b² to find 87².
7. 7.Use (a − b)² = a² − 2ab + b² to find 16².
8. 8.Use (a + b)² = a² + 2ab + b² to find 93².
9. 9.Use a² − b² = (a + b)(a − b) to find 31² − 11².
10. 10.Use a² − b² = (a + b)(a − b) to find 69² − 12².
11. 11.Use (a − b)² = a² − 2ab + b² to find 31².
12. 12.Use (a + b)(a − b) = a² − b² to find 63 × 57.
13. 13.If a − b = 5 and ab = 14, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 21 × 19.
15. 15.Use (a + b)(a − b) = a² − b² to find 57 × 43.
16. 16.Use (a − b)² = a² − 2ab + b² to find 44².
17. 17.Use (a − b)² = a² − 2ab + b² to find 22².
18. 18.Use (a + b)(a − b) = a² − b² to find 56 × 44.
19. 19.If a + b = 10 and ab = 21, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 98² − 52².
21. 21.Use a² − b² = (a + b)(a − b) to find 49² − 31².
22. 22.Use a² − b² = (a + b)(a − b) to find 83² − 28².
23. 23.Use (a − b)² = a² − 2ab + b² to find 37².
24. 24.If a + b = 14 and ab = 48, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 95² − 43².
26. 26.Find the value of x² − y² when x = 3 and y = 1.
27. 27.Use (a − b)² = a² − 2ab + b² to find 67².
28. 28.Use (a + b)² = a² + 2ab + b² to find 89².
29. 29.Use (a + b)² = a² + 2ab + b² to find 59².
30. 30.Use (a + b)² = a² + 2ab + b² to find 61².
31. 31.If a − b = 1 and ab = 20, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 97 × 83.
33. 33.Use (a + b)(a − b) = a² − b² to find 84 × 76.
34. 34.Find the value of x² − y² when x = 6 and y = 4.
35. 35.Use (a + b)² = a² + 2ab + b² to find 62².
36. 36.If a − b = 1 and ab = 30, what is a² + b²?
37. 37.If a + b = 14 and ab = 40, what is a² + b²?
38. 38.Find the value of x² − 2xy + y² when x = 14 and y = 1.
39. 39.Use (a − b)² = a² − 2ab + b² to find 13².
40. 40.Find the value of x² − 2xy + y² when x = 6 and y = 1.

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