Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 538 · 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 93² − 27².
2. 2.Use (a + b)² = a² + 2ab + b² to find 102².
3. 3.Use (a − b)² = a² − 2ab + b² to find 31².
4. 4.Use (a − b)² = a² − 2ab + b² to find 69².
5. 5.Use (a + b)² = a² + 2ab + b² to find 16².
6. 6.Use (a − b)² = a² − 2ab + b² to find 33².
7. 7.Use (a − b)² = a² − 2ab + b² to find 41².
8. 8.Use a² − b² = (a + b)(a − b) to find 20² − 4².
9. 9.Find the value of x² − y² when x = 7 and y = 1.
10. 10.Use a² − b² = (a + b)(a − b) to find 27² − 16².
11. 11.Use (a − b)² = a² − 2ab + b² to find 27².
12. 12.Use (a + b)² = a² + 2ab + b² to find 91².
13. 13.Use a² − b² = (a + b)(a − b) to find 91² − 67².
14. 14.If a + b = 12 and ab = 35, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 95² − 56².
16. 16.Use (a + b)(a − b) = a² − b² to find 62 × 58.
17. 17.Use a² − b² = (a + b)(a − b) to find 87² − 59².
18. 18.Use (a + b)(a − b) = a² − b² to find 88 × 72.
19. 19.Use (a − b)² = a² − 2ab + b² to find 83².
20. 20.Find the value of x² + 2xy + y² when x = 7 and y = 5.
21. 21.Use (a + b)² = a² + 2ab + b² to find 44².
22. 22.Use (a + b)(a − b) = a² − b² to find 39 × 21.
23. 23.If a − b = 2 and ab = 8, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 73 × 67.
25. 25.If a − b = 1 and ab = 12, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 39².
27. 27.Use (a + b)(a − b) = a² − b² to find 42 × 38.
28. 28.Use (a − b)² = a² − 2ab + b² to find 55².
29. 29.Use (a + b)(a − b) = a² − b² to find 64 × 56.
30. 30.If a + b = 18 and ab = 77, what is a² + b²?
31. 31.If a + b = 5 and ab = 4, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 36².
33. 33.Find the value of x² − y² when x = 10 and y = 2.
34. 34.Use (a − b)² = a² − 2ab + b² to find 89².
35. 35.Find the value of x² − 2xy + y² when x = 11 and y = 9.
36. 36.Use a² − b² = (a + b)(a − b) to find 70² − 27².
37. 37.Use (a − b)² = a² − 2ab + b² to find 11².
38. 38.If a + b = 6 and ab = 8, what is a² + b²?
39. 39.If a + b = 7 and ab = 12, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 22².

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