Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 508 · 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 73 × 67.
2. 2.Use (a − b)² = a² − 2ab + b² to find 28².
3. 3.Use (a + b)² = a² + 2ab + b² to find 21².
4. 4.Use (a − b)² = a² − 2ab + b² to find 94².
5. 5.Use (a + b)² = a² + 2ab + b² to find 106².
6. 6.If a + b = 23 and ab = 132, what is a² + b²?
7. 7.If a − b = 4 and ab = 12, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 49 × 31.
9. 9.Use (a − b)² = a² − 2ab + b² to find 79².
10. 10.Use (a + b)² = a² + 2ab + b² to find 17².
11. 11.Use (a + b)(a − b) = a² − b² to find 87 × 73.
12. 12.Find the value of x² + 2xy + y² when x = 13 and y = 1.
13. 13.Use a² − b² = (a + b)(a − b) to find 99² − 6².
14. 14.Use (a − b)² = a² − 2ab + b² to find 52².
15. 15.Use (a + b)(a − b) = a² − b² to find 38 × 22.
16. 16.Use a² − b² = (a + b)(a − b) to find 45² − 31².
17. 17.Use (a + b)(a − b) = a² − b² to find 91 × 89.
18. 18.Use (a − b)² = a² − 2ab + b² to find 47².
19. 19.Use (a + b)(a − b) = a² − b² to find 81 × 79.
20. 20.Use (a + b)² = a² + 2ab + b² to find 19².
21. 21.Use (a + b)² = a² + 2ab + b² to find 27².
22. 22.Use (a + b)² = a² + 2ab + b² to find 23².
23. 23.Use a² − b² = (a + b)(a − b) to find 50² − 11².
24. 24.If a − b = 3 and ab = 10, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 72².
26. 26.Use (a + b)(a − b) = a² − b² to find 72 × 68.
27. 27.Use (a + b)(a − b) = a² − b² to find 75 × 65.
28. 28.Find the value of x² − 2xy + y² when x = 13 and y = 12.
29. 29.Use (a + b)(a − b) = a² − b² to find 86 × 74.
30. 30.Use (a + b)(a − b) = a² − b² to find 92 × 88.
31. 31.Use a² − b² = (a + b)(a − b) to find 95² − 84².
32. 32.Use (a + b)(a − b) = a² − b² to find 69 × 51.
33. 33.Use (a + b)² = a² + 2ab + b² to find 22².
34. 34.If a + b = 5 and ab = 4, what is a² + b²?
35. 35.If a + b = 5 and ab = 6, what is a² + b²?
36. 36.If a − b = 11 and ab = 12, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 87².
38. 38.Use a² − b² = (a + b)(a − b) to find 75² − 68².
39. 39.Use (a + b)² = a² + 2ab + b² to find 101².
40. 40.Use a² − b² = (a + b)(a − b) to find 71² − 21².

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