Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 28 · 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 91 × 89.
2. 2.Use (a + b)² = a² + 2ab + b² to find 29².
3. 3.Use a² − b² = (a + b)(a − b) to find 31² − 4².
4. 4.Use a² − b² = (a + b)(a − b) to find 49² − 40².
5. 5.Use (a − b)² = a² − 2ab + b² to find 88².
6. 6.If a + b = 7 and ab = 12, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 60² − 2².
8. 8.Use (a + b)² = a² + 2ab + b² to find 101².
9. 9.Use a² − b² = (a + b)(a − b) to find 85² − 31².
10. 10.Use (a + b)² = a² + 2ab + b² to find 45².
11. 11.Use (a − b)² = a² − 2ab + b² to find 59².
12. 12.Use (a + b)² = a² + 2ab + b² to find 102².
13. 13.Use (a + b)(a − b) = a² − b² to find 98 × 82.
14. 14.Find the value of x² + 2xy + y² when x = 5 and y = 4.
15. 15.Use (a + b)(a − b) = a² − b² to find 79 × 61.
16. 16.Use (a + b)² = a² + 2ab + b² to find 56².
17. 17.If a − b = 5 and ab = 6, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 107².
19. 19.Use (a + b)(a − b) = a² − b² to find 66 × 54.
20. 20.Use (a − b)² = a² − 2ab + b² to find 38².
21. 21.Use a² − b² = (a + b)(a − b) to find 32² − 16².
22. 22.Use (a − b)² = a² − 2ab + b² to find 21².
23. 23.Find the value of x² − 2xy + y² when x = 7 and y = 1.
24. 24.Use (a + b)² = a² + 2ab + b² to find 34².
25. 25.Use (a + b)(a − b) = a² − b² to find 29 × 11.
26. 26.Find the value of x² + 2xy + y² when x = 14 and y = 10.
27. 27.Use (a − b)² = a² − 2ab + b² to find 84².
28. 28.Use (a + b)² = a² + 2ab + b² to find 84².
29. 29.Use a² − b² = (a + b)(a − b) to find 33² − 26².
30. 30.Use (a + b)(a − b) = a² − b² to find 93 × 87.
31. 31.Use (a + b)(a − b) = a² − b² to find 48 × 32.
32. 32.Find the value of x² + 2xy + y² when x = 14 and y = 1.
33. 33.Use (a + b)² = a² + 2ab + b² to find 83².
34. 34.If a − b = 1 and ab = 2, what is a² + b²?
35. 35.If a + b = 17 and ab = 70, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 73².
37. 37.If a + b = 3 and ab = 2, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 48².
39. 39.Use (a + b)(a − b) = a² − b² to find 31 × 29.
40. 40.Use a² − b² = (a + b)(a − b) to find 98² − 77².

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