Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 121 · 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.Find the value of x² − 2xy + y² when x = 9 and y = 4.
2. 2.If a − b = 2 and ab = 24, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 39 × 21.
4. 4.Use (a + b)(a − b) = a² − b² to find 76 × 64.
5. 5.Use a² − b² = (a + b)(a − b) to find 74² − 61².
6. 6.Use (a + b)² = a² + 2ab + b² to find 71².
7. 7.Use (a − b)² = a² − 2ab + b² to find 17².
8. 8.Use (a + b)(a − b) = a² − b² to find 32 × 28.
9. 9.Use a² − b² = (a + b)(a − b) to find 73² − 15².
10. 10.Use (a + b)(a − b) = a² − b² to find 95 × 85.
11. 11.Use (a + b)² = a² + 2ab + b² to find 69².
12. 12.Use (a + b)² = a² + 2ab + b² to find 13².
13. 13.Use (a − b)² = a² − 2ab + b² to find 59².
14. 14.Use (a + b)(a − b) = a² − b² to find 94 × 86.
15. 15.Use (a + b)² = a² + 2ab + b² to find 36².
16. 16.Use a² − b² = (a + b)(a − b) to find 67² − 10².
17. 17.Use a² − b² = (a + b)(a − b) to find 96² − 48².
18. 18.Use (a + b)(a − b) = a² − b² to find 92 × 88.
19. 19.Find the value of x² − y² when x = 9 and y = 2.
20. 20.Find the value of x² − 2xy + y² when x = 9 and y = 7.
21. 21.Use (a − b)² = a² − 2ab + b² to find 16².
22. 22.Use (a + b)² = a² + 2ab + b² to find 56².
23. 23.Use (a + b)² = a² + 2ab + b² to find 63².
24. 24.Use (a − b)² = a² − 2ab + b² to find 63².
25. 25.Use (a − b)² = a² − 2ab + b² to find 31².
26. 26.Use (a − b)² = a² − 2ab + b² to find 66².
27. 27.Use (a + b)(a − b) = a² − b² to find 63 × 57.
28. 28.Use (a + b)² = a² + 2ab + b² to find 58².
29. 29.If a − b = 11 and ab = 12, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 46² − 14².
31. 31.Find the value of x² + 2xy + y² when x = 13 and y = 5.
32. 32.Use (a + b)² = a² + 2ab + b² to find 32².
33. 33.Use a² − b² = (a + b)(a − b) to find 88² − 22².
34. 34.If a − b = 2 and ab = 120, what is a² + b²?
35. 35.If a − b = 1 and ab = 12, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 103 × 97.
37. 37.Use a² − b² = (a + b)(a − b) to find 50² − 34².
38. 38.Use a² − b² = (a + b)(a − b) to find 94² − 44².
39. 39.Use (a − b)² = a² − 2ab + b² to find 46².
40. 40.If a − b = 3 and ab = 70, what is a² + b²?

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