Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 554 · 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 41² − 32².
2. 2.Find the value of x² − y² when x = 15 and y = 2.
3. 3.Use (a + b)² = a² + 2ab + b² to find 88².
4. 4.If a + b = 13 and ab = 22, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 42².
6. 6.If a − b = 3 and ab = 108, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 93² − 74².
8. 8.Use (a + b)(a − b) = a² − b² to find 104 × 96.
9. 9.Use a² − b² = (a + b)(a − b) to find 83² − 59².
10. 10.Use (a + b)² = a² + 2ab + b² to find 58².
11. 11.Use (a + b)² = a² + 2ab + b² to find 97².
12. 12.Use (a + b)² = a² + 2ab + b² to find 17².
13. 13.Use (a + b)² = a² + 2ab + b² to find 31².
14. 14.Use (a + b)² = a² + 2ab + b² to find 96².
15. 15.Use (a − b)² = a² − 2ab + b² to find 38².
16. 16.Use (a + b)² = a² + 2ab + b² to find 67².
17. 17.Use (a + b)(a − b) = a² − b² to find 86 × 74.
18. 18.Use (a + b)² = a² + 2ab + b² to find 22².
19. 19.Use (a − b)² = a² − 2ab + b² to find 43².
20. 20.Use (a + b)² = a² + 2ab + b² to find 86².
21. 21.Use a² − b² = (a + b)(a − b) to find 28² − 11².
22. 22.Find the value of x² + 2xy + y² when x = 4 and y = 1.
23. 23.Use a² − b² = (a + b)(a − b) to find 25² − 14².
24. 24.Use (a − b)² = a² − 2ab + b² to find 82².
25. 25.Use (a + b)(a − b) = a² − b² to find 24 × 16.
26. 26.Use (a − b)² = a² − 2ab + b² to find 64².
27. 27.Use (a − b)² = a² − 2ab + b² to find 35².
28. 28.Use (a − b)² = a² − 2ab + b² to find 88².
29. 29.Use (a − b)² = a² − 2ab + b² to find 51².
30. 30.Find the value of x² + 2xy + y² when x = 14 and y = 3.
31. 31.Use a² − b² = (a + b)(a − b) to find 92² − 46².
32. 32.Use (a − b)² = a² − 2ab + b² to find 56².
33. 33.Use a² − b² = (a + b)(a − b) to find 53² − 43².
34. 34.Use a² − b² = (a + b)(a − b) to find 47² − 39².
35. 35.If a + b = 14 and ab = 40, what is a² + b²?
36. 36.If a − b = 1 and ab = 2, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 24².
38. 38.Use a² − b² = (a + b)(a − b) to find 32² − 22².
39. 39.If a − b = 2 and ab = 120, what is a² + b²?
40. 40.Find the value of x² + 2xy + y² when x = 7 and y = 1.

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