Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 739 · 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 a² − b² = (a + b)(a − b) to find 82² − 8².
2. 2.Find the value of x² − y² when x = 12 and y = 1.
3. 3.Use a² − b² = (a + b)(a − b) to find 82² − 26².
4. 4.Use (a + b)(a − b) = a² − b² to find 91 × 89.
5. 5.If a − b = 5 and ab = 36, what is a² + b²?
6. 6.If a − b = 2 and ab = 3, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 98² − 87².
8. 8.Use (a + b)² = a² + 2ab + b² to find 83².
9. 9.Use (a − b)² = a² − 2ab + b² to find 69².
10. 10.Use a² − b² = (a + b)(a − b) to find 54² − 13².
11. 11.Use a² − b² = (a + b)(a − b) to find 44² − 30².
12. 12.If a + b = 3 and ab = 2, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 68².
14. 14.Use (a − b)² = a² − 2ab + b² to find 62².
15. 15.If a + b = 5 and ab = 4, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 105 × 95.
17. 17.Use (a + b)(a − b) = a² − b² to find 62 × 58.
18. 18.Use (a + b)(a − b) = a² − b² to find 21 × 19.
19. 19.Use (a − b)² = a² − 2ab + b² to find 74².
20. 20.If a − b = 1 and ab = 12, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 16².
22. 22.Use (a + b)² = a² + 2ab + b² to find 47².
23. 23.Find the value of x² + 2xy + y² when x = 9 and y = 2.
24. 24.Use a² − b² = (a + b)(a − b) to find 31² − 9².
25. 25.Use (a + b)(a − b) = a² − b² to find 57 × 43.
26. 26.Use (a − b)² = a² − 2ab + b² to find 18².
27. 27.Use (a − b)² = a² − 2ab + b² to find 61².
28. 28.Use (a − b)² = a² − 2ab + b² to find 15².
29. 29.Use (a + b)² = a² + 2ab + b² to find 17².
30. 30.Use (a + b)² = a² + 2ab + b² to find 77².
31. 31.Use (a + b)(a − b) = a² − b² to find 51 × 49.
32. 32.Use (a + b)(a − b) = a² − b² to find 27 × 13.
33. 33.Use (a + b)(a − b) = a² − b² to find 67 × 53.
34. 34.If a + b = 6 and ab = 5, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 32 × 28.
36. 36.If a − b = 7 and ab = 8, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 66².
38. 38.Find the value of x² − 2xy + y² when x = 13 and y = 6.
39. 39.Use (a + b)(a − b) = a² − b² to find 26 × 14.
40. 40.Find the value of x² − 2xy + y² when x = 7 and y = 1.

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