Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 64 · 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 53².
2. 2.Use (a + b)² = a² + 2ab + b² to find 93².
3. 3.Use (a − b)² = a² − 2ab + b² to find 13².
4. 4.Use (a + b)² = a² + 2ab + b² to find 86².
5. 5.Use (a + b)² = a² + 2ab + b² to find 74².
6. 6.Use (a + b)(a − b) = a² − b² to find 62 × 58.
7. 7.If a − b = 4 and ab = 5, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 41² − 13².
9. 9.Use (a − b)² = a² − 2ab + b² to find 59².
10. 10.Use (a + b)² = a² + 2ab + b² to find 13².
11. 11.Use (a + b)(a − b) = a² − b² to find 31 × 29.
12. 12.Use (a + b)² = a² + 2ab + b² to find 67².
13. 13.Use a² − b² = (a + b)(a − b) to find 46² − 35².
14. 14.Use (a + b)(a − b) = a² − b² to find 67 × 53.
15. 15.Use (a + b)² = a² + 2ab + b² to find 29².
16. 16.Use a² − b² = (a + b)(a − b) to find 75² − 45².
17. 17.Use (a − b)² = a² − 2ab + b² to find 29².
18. 18.If a − b = 1 and ab = 12, what is a² + b²?
19. 19.Use (a + b)(a − b) = a² − b² to find 58 × 42.
20. 20.Use a² − b² = (a + b)(a − b) to find 93² − 2².
21. 21.Use a² − b² = (a + b)(a − b) to find 33² − 4².
22. 22.Use (a − b)² = a² − 2ab + b² to find 42².
23. 23.Use (a + b)² = a² + 2ab + b² to find 19².
24. 24.If a + b = 17 and ab = 72, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 87 × 73.
26. 26.Use (a − b)² = a² − 2ab + b² to find 23².
27. 27.If a − b = 8 and ab = 33, what is a² + b²?
28. 28.If a + b = 13 and ab = 22, what is a² + b²?
29. 29.Find the value of x² − 2xy + y² when x = 8 and y = 7.
30. 30.Use (a + b)(a − b) = a² − b² to find 106 × 94.
31. 31.Find the value of x² − 2xy + y² when x = 4 and y = 3.
32. 32.Use a² − b² = (a + b)(a − b) to find 68² − 39².
33. 33.Use (a + b)(a − b) = a² − b² to find 109 × 91.
34. 34.If a − b = 2 and ab = 3, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 66².
36. 36.Find the value of x² − y² when x = 3 and y = 2.
37. 37.Use (a − b)² = a² − 2ab + b² to find 49².
38. 38.Use (a − b)² = a² − 2ab + b² to find 15².
39. 39.Use (a − b)² = a² − 2ab + b² to find 62².
40. 40.Find the value of x² − 2xy + y² when x = 8 and y = 3.

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