Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 920 · 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)(a − b) = a² − b² to find 72 × 68.
2. 2.Use (a − b)² = a² − 2ab + b² to find 96².
3. 3.Use (a + b)² = a² + 2ab + b² to find 62².
4. 4.Use (a + b)² = a² + 2ab + b² to find 28².
5. 5.Use (a + b)(a − b) = a² − b² to find 25 × 15.
6. 6.Find the value of x² − y² when x = 11 and y = 10.
7. 7.Use a² − b² = (a + b)(a − b) to find 82² − 42².
8. 8.Find the value of x² + 2xy + y² when x = 8 and y = 4.
9. 9.Use (a + b)² = a² + 2ab + b² to find 38².
10. 10.Use (a + b)(a − b) = a² − b² to find 29 × 11.
11. 11.Use (a + b)(a − b) = a² − b² to find 107 × 93.
12. 12.Use (a + b)(a − b) = a² − b² to find 78 × 62.
13. 13.If a + b = 14 and ab = 45, what is a² + b²?
14. 14.Find the value of x² − y² when x = 15 and y = 4.
15. 15.Use a² − b² = (a + b)(a − b) to find 78² − 1².
16. 16.Use (a − b)² = a² − 2ab + b² to find 97².
17. 17.Use (a + b)² = a² + 2ab + b² to find 55².
18. 18.Use (a + b)² = a² + 2ab + b² to find 75².
19. 19.Use (a − b)² = a² − 2ab + b² to find 33².
20. 20.Use (a + b)(a − b) = a² − b² to find 34 × 26.
21. 21.Use (a − b)² = a² − 2ab + b² to find 27².
22. 22.If a − b = 10 and ab = 11, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 13².
24. 24.If a − b = 8 and ab = 48, what is a² + b²?
25. 25.If a + b = 8 and ab = 15, what is a² + b²?
26. 26.If a + b = 11 and ab = 24, what is a² + b²?
27. 27.Find the value of x² + 2xy + y² when x = 15 and y = 3.
28. 28.Use (a + b)² = a² + 2ab + b² to find 53².
29. 29.Use a² − b² = (a + b)(a − b) to find 66² − 55².
30. 30.If a + b = 5 and ab = 6, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 19².
32. 32.Use (a + b)² = a² + 2ab + b² to find 107².
33. 33.Use (a + b)² = a² + 2ab + b² to find 106².
34. 34.Use (a + b)(a − b) = a² − b² to find 104 × 96.
35. 35.Use (a + b)(a − b) = a² − b² to find 88 × 72.
36. 36.Use a² − b² = (a + b)(a − b) to find 95² − 64².
37. 37.Use (a − b)² = a² − 2ab + b² to find 22².
38. 38.Find the value of x² − y² when x = 6 and y = 4.
39. 39.Use (a + b)² = a² + 2ab + b² to find 37².
40. 40.Use (a + b)² = a² + 2ab + b² to find 41².

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