Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 114 · 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.Find the value of x² − 2xy + y² when x = 3 and y = 1.
2. 2.Find the value of x² − y² when x = 5 and y = 1.
3. 3.Use (a + b)² = a² + 2ab + b² to find 91².
4. 4.Find the value of x² + 2xy + y² when x = 5 and y = 2.
5. 5.Use (a + b)² = a² + 2ab + b² to find 16².
6. 6.Use (a + b)(a − b) = a² − b² to find 58 × 42.
7. 7.If a + b = 11 and ab = 28, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 80² − 22².
9. 9.If a − b = 4 and ab = 45, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 67².
11. 11.Use (a − b)² = a² − 2ab + b² to find 13².
12. 12.Find the value of x² − y² when x = 5 and y = 3.
13. 13.Use (a − b)² = a² − 2ab + b² to find 89².
14. 14.Use (a − b)² = a² − 2ab + b² to find 15².
15. 15.Find the value of x² − y² when x = 9 and y = 8.
16. 16.Use a² − b² = (a + b)(a − b) to find 81² − 68².
17. 17.Use (a + b)² = a² + 2ab + b² to find 107².
18. 18.Use (a − b)² = a² − 2ab + b² to find 42².
19. 19.Use (a − b)² = a² − 2ab + b² to find 43².
20. 20.If a − b = 4 and ab = 21, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 99².
22. 22.Use a² − b² = (a + b)(a − b) to find 22² − 17².
23. 23.Use a² − b² = (a + b)(a − b) to find 63² − 39².
24. 24.If a + b = 13 and ab = 42, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 31² − 21².
26. 26.Use (a − b)² = a² − 2ab + b² to find 46².
27. 27.Use a² − b² = (a + b)(a − b) to find 20² − 4².
28. 28.Use (a + b)² = a² + 2ab + b² to find 101².
29. 29.Find the value of x² − y² when x = 14 and y = 4.
30. 30.Use a² − b² = (a + b)(a − b) to find 93² − 37².
31. 31.Use a² − b² = (a + b)(a − b) to find 83² − 67².
32. 32.Use (a + b)² = a² + 2ab + b² to find 35².
33. 33.If a + b = 21 and ab = 108, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 49 × 31.
35. 35.Use a² − b² = (a + b)(a − b) to find 26² − 13².
36. 36.Use (a − b)² = a² − 2ab + b² to find 65².
37. 37.Use (a + b)² = a² + 2ab + b² to find 79².
38. 38.Use (a + b)² = a² + 2ab + b² to find 96².
39. 39.Find the value of x² − 2xy + y² when x = 8 and y = 3.
40. 40.Use a² − b² = (a + b)(a − b) to find 29² − 9².

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