Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 958 · 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)² = a² − 2ab + b² to find 61².
2. 2.Use (a + b)(a − b) = a² − b² to find 23 × 17.
3. 3.Use (a + b)(a − b) = a² − b² to find 53 × 47.
4. 4.Use (a − b)² = a² − 2ab + b² to find 22².
5. 5.Use (a + b)² = a² + 2ab + b² to find 38².
6. 6.Use (a + b)(a − b) = a² − b² to find 93 × 87.
7. 7.Use (a + b)(a − b) = a² − b² to find 31 × 29.
8. 8.Find the value of x² − 2xy + y² when x = 9 and y = 1.
9. 9.Use (a + b)(a − b) = a² − b² to find 69 × 51.
10. 10.Use (a − b)² = a² − 2ab + b² to find 72².
11. 11.If a + b = 17 and ab = 60, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 58 × 42.
13. 13.If a − b = 5 and ab = 6, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 13².
15. 15.Find the value of x² + 2xy + y² when x = 6 and y = 4.
16. 16.Use a² − b² = (a + b)(a − b) to find 60² − 24².
17. 17.Use (a + b)² = a² + 2ab + b² to find 85².
18. 18.Use (a + b)² = a² + 2ab + b² to find 71².
19. 19.Use a² − b² = (a + b)(a − b) to find 65² − 35².
20. 20.Find the value of x² − 2xy + y² when x = 7 and y = 3.
21. 21.Use (a + b)² = a² + 2ab + b² to find 91².
22. 22.Use (a + b)² = a² + 2ab + b² to find 27².
23. 23.Find the value of x² + 2xy + y² when x = 15 and y = 7.
24. 24.Use (a − b)² = a² − 2ab + b² to find 91².
25. 25.If a − b = 1 and ab = 6, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 14².
27. 27.Use a² − b² = (a + b)(a − b) to find 37² − 26².
28. 28.Use (a + b)² = a² + 2ab + b² to find 52².
29. 29.Use a² − b² = (a + b)(a − b) to find 84² − 9².
30. 30.Use (a + b)(a − b) = a² − b² to find 88 × 72.
31. 31.If a + b = 3 and ab = 2, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 31².
33. 33.Use (a − b)² = a² − 2ab + b² to find 56².
34. 34.If a + b = 10 and ab = 24, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 27 × 13.
36. 36.Find the value of x² − 2xy + y² when x = 11 and y = 10.
37. 37.Find the value of x² − 2xy + y² when x = 11 and y = 3.
38. 38.Use a² − b² = (a + b)(a − b) to find 77² − 68².
39. 39.If a − b = 4 and ab = 32, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 98² − 96².

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