Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 165 · 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.If a + b = 23 and ab = 132, what is a² + b²?
2. 2.Find the value of x² + 2xy + y² when x = 13 and y = 3.
3. 3.Use a² − b² = (a + b)(a − b) to find 73² − 32².
4. 4.Use (a + b)² = a² + 2ab + b² to find 87².
5. 5.Use (a + b)(a − b) = a² − b² to find 102 × 98.
6. 6.Use (a + b)(a − b) = a² − b² to find 49 × 31.
7. 7.Use (a − b)² = a² − 2ab + b² to find 25².
8. 8.Find the value of x² − y² when x = 5 and y = 4.
9. 9.Find the value of x² + 2xy + y² when x = 5 and y = 4.
10. 10.Use (a − b)² = a² − 2ab + b² to find 87².
11. 11.Use (a + b)(a − b) = a² − b² to find 36 × 24.
12. 12.Find the value of x² − y² when x = 4 and y = 2.
13. 13.Use (a + b)² = a² + 2ab + b² to find 63².
14. 14.Use (a + b)² = a² + 2ab + b² to find 71².
15. 15.Use a² − b² = (a + b)(a − b) to find 59² − 46².
16. 16.Use (a + b)² = a² + 2ab + b² to find 57².
17. 17.Use a² − b² = (a + b)(a − b) to find 74² − 19².
18. 18.If a + b = 12 and ab = 11, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 21² − 6².
20. 20.Use a² − b² = (a + b)(a − b) to find 74² − 66².
21. 21.Use a² − b² = (a + b)(a − b) to find 60² − 58².
22. 22.Use (a − b)² = a² − 2ab + b² to find 31².
23. 23.Use (a − b)² = a² − 2ab + b² to find 76².
24. 24.If a − b = 1 and ab = 12, what is a² + b²?
25. 25.Find the value of x² − y² when x = 7 and y = 3.
26. 26.Use a² − b² = (a + b)(a − b) to find 58² − 46².
27. 27.Use (a + b)² = a² + 2ab + b² to find 56².
28. 28.Use (a + b)(a − b) = a² − b² to find 93 × 87.
29. 29.Use (a + b)² = a² + 2ab + b² to find 16².
30. 30.Use (a − b)² = a² − 2ab + b² to find 81².
31. 31.Use (a − b)² = a² − 2ab + b² to find 53².
32. 32.Use a² − b² = (a + b)(a − b) to find 33² − 32².
33. 33.Find the value of x² + 2xy + y² when x = 15 and y = 3.
34. 34.Use (a − b)² = a² − 2ab + b² to find 47².
35. 35.If a − b = 5 and ab = 6, what is a² + b²?
36. 36.If a + b = 14 and ab = 48, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 16².
38. 38.Use (a − b)² = a² − 2ab + b² to find 17².
39. 39.If a − b = 1 and ab = 110, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 22² − 18².

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