Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 556 · 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 60² − 53².
2. 2.Find the value of x² + 2xy + y² when x = 7 and y = 1.
3. 3.Use (a + b)(a − b) = a² − b² to find 22 × 18.
4. 4.If a + b = 12 and ab = 20, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 31² − 7².
6. 6.Use (a + b)² = a² + 2ab + b² to find 81².
7. 7.Use (a − b)² = a² − 2ab + b² to find 59².
8. 8.Find the value of x² − y² when x = 10 and y = 8.
9. 9.Use (a + b)² = a² + 2ab + b² to find 56².
10. 10.Use (a + b)(a − b) = a² − b² to find 104 × 96.
11. 11.Use (a + b)² = a² + 2ab + b² to find 95².
12. 12.Find the value of x² − 2xy + y² when x = 11 and y = 8.
13. 13.If a − b = 3 and ab = 54, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 98².
15. 15.Find the value of x² + 2xy + y² when x = 9 and y = 4.
16. 16.Use (a − b)² = a² − 2ab + b² to find 61².
17. 17.Use a² − b² = (a + b)(a − b) to find 99² − 69².
18. 18.If a − b = 3 and ab = 4, what is a² + b²?
19. 19.Use (a + b)(a − b) = a² − b² to find 21 × 19.
20. 20.Use (a − b)² = a² − 2ab + b² to find 45².
21. 21.Find the value of x² − y² when x = 12 and y = 1.
22. 22.Use (a − b)² = a² − 2ab + b² to find 35².
23. 23.Use (a + b)(a − b) = a² − b² to find 82 × 78.
24. 24.Use (a − b)² = a² − 2ab + b² to find 72².
25. 25.Use (a − b)² = a² − 2ab + b² to find 88².
26. 26.Use (a + b)(a − b) = a² − b² to find 36 × 24.
27. 27.Use a² − b² = (a + b)(a − b) to find 63² − 46².
28. 28.Use a² − b² = (a + b)(a − b) to find 79² − 26².
29. 29.Use a² − b² = (a + b)(a − b) to find 31² − 18².
30. 30.Use (a + b)² = a² + 2ab + b² to find 35².
31. 31.If a − b = 3 and ab = 10, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 34² − 2².
33. 33.Use (a + b)² = a² + 2ab + b² to find 84².
34. 34.Find the value of x² − 2xy + y² when x = 12 and y = 4.
35. 35.Use (a − b)² = a² − 2ab + b² to find 65².
36. 36.Use (a − b)² = a² − 2ab + b² to find 71².
37. 37.If a − b = 9 and ab = 10, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 56² − 22².
39. 39.Use (a + b)² = a² + 2ab + b² to find 108².
40. 40.Use (a + b)(a − b) = a² − b² to find 87 × 73.

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