Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 595 · 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 94².
2. 2.Use (a + b)(a − b) = a² − b² to find 22 × 18.
3. 3.Use (a − b)² = a² − 2ab + b² to find 67².
4. 4.Use (a − b)² = a² − 2ab + b² to find 89².
5. 5.Find the value of x² + 2xy + y² when x = 8 and y = 3.
6. 6.Use a² − b² = (a + b)(a − b) to find 89² − 24².
7. 7.Use (a + b)² = a² + 2ab + b² to find 62².
8. 8.Use a² − b² = (a + b)(a − b) to find 95² − 75².
9. 9.If a + b = 16 and ab = 48, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 35².
11. 11.Use a² − b² = (a + b)(a − b) to find 25² − 3².
12. 12.If a − b = 2 and ab = 120, what is a² + b²?
13. 13.Find the value of x² − 2xy + y² when x = 13 and y = 11.
14. 14.Use (a + b)² = a² + 2ab + b² to find 59².
15. 15.Use (a − b)² = a² − 2ab + b² to find 56².
16. 16.Use (a + b)² = a² + 2ab + b² to find 105².
17. 17.If a − b = 6 and ab = 16, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 71 × 69.
19. 19.Use (a + b)(a − b) = a² − b² to find 68 × 52.
20. 20.Use (a − b)² = a² − 2ab + b² to find 97².
21. 21.Use (a + b)² = a² + 2ab + b² to find 26².
22. 22.If a + b = 9 and ab = 20, what is a² + b²?
23. 23.Find the value of x² − y² when x = 3 and y = 1.
24. 24.Use (a − b)² = a² − 2ab + b² to find 69².
25. 25.Find the value of x² + 2xy + y² when x = 15 and y = 6.
26. 26.Use (a + b)(a − b) = a² − b² to find 79 × 61.
27. 27.Use a² − b² = (a + b)(a − b) to find 95² − 68².
28. 28.Use a² − b² = (a + b)(a − b) to find 23² − 2².
29. 29.Use (a − b)² = a² − 2ab + b² to find 47².
30. 30.Find the value of x² − 2xy + y² when x = 6 and y = 4.
31. 31.Find the value of x² + 2xy + y² when x = 13 and y = 6.
32. 32.Use (a + b)(a − b) = a² − b² to find 92 × 88.
33. 33.Use (a + b)² = a² + 2ab + b² to find 36².
34. 34.Use (a + b)(a − b) = a² − b² to find 59 × 41.
35. 35.Use (a − b)² = a² − 2ab + b² to find 49².
36. 36.Find the value of x² − y² when x = 13 and y = 4.
37. 37.Find the value of x² − y² when x = 10 and y = 1.
38. 38.If a + b = 7 and ab = 10, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 62² − 15².
40. 40.Use a² − b² = (a + b)(a − b) to find 32² − 15².

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