Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 627 · 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 22².
2. 2.If a − b = 4 and ab = 5, what is a² + b²?
3. 3.Use (a + b)² = a² + 2ab + b² to find 68².
4. 4.Use (a + b)² = a² + 2ab + b² to find 64².
5. 5.Find the value of x² − 2xy + y² when x = 7 and y = 2.
6. 6.Use (a + b)² = a² + 2ab + b² to find 37².
7. 7.Use a² − b² = (a + b)(a − b) to find 50² − 5².
8. 8.Use (a + b)² = a² + 2ab + b² to find 32².
9. 9.Use (a + b)² = a² + 2ab + b² to find 31².
10. 10.If a + b = 5 and ab = 4, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 24².
12. 12.Find the value of x² − y² when x = 15 and y = 14.
13. 13.If a − b = 1 and ab = 6, what is a² + b²?
14. 14.If a − b = 2 and ab = 3, what is a² + b²?
15. 15.Use (a + b)(a − b) = a² − b² to find 27 × 13.
16. 16.Use (a + b)² = a² + 2ab + b² to find 88².
17. 17.Find the value of x² − 2xy + y² when x = 10 and y = 2.
18. 18.Use a² − b² = (a + b)(a − b) to find 53² − 47².
19. 19.If a + b = 6 and ab = 5, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 97².
21. 21.Use a² − b² = (a + b)(a − b) to find 29² − 5².
22. 22.Use (a + b)(a − b) = a² − b² to find 93 × 87.
23. 23.Find the value of x² − 2xy + y² when x = 10 and y = 1.
24. 24.Use a² − b² = (a + b)(a − b) to find 39² − 10².
25. 25.Use (a + b)(a − b) = a² − b² to find 79 × 61.
26. 26.If a + b = 9 and ab = 8, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 32².
28. 28.If a + b = 3 and ab = 2, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 34² − 30².
30. 30.Use (a + b)² = a² + 2ab + b² to find 26².
31. 31.Use a² − b² = (a + b)(a − b) to find 57² − 14².
32. 32.Use (a + b)(a − b) = a² − b² to find 41 × 39.
33. 33.Use (a − b)² = a² − 2ab + b² to find 44².
34. 34.Use (a + b)² = a² + 2ab + b² to find 12².
35. 35.Use a² − b² = (a + b)(a − b) to find 82² − 13².
36. 36.Use a² − b² = (a + b)(a − b) to find 32² − 1².
37. 37.Use (a − b)² = a² − 2ab + b² to find 37².
38. 38.Use (a + b)(a − b) = a² − b² to find 105 × 95.
39. 39.If a + b = 15 and ab = 44, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 49 × 31.

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