Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 933 · 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 = 10 and ab = 21, what is a² + b²?
2. 2.If a − b = 1 and ab = 2, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 14².
4. 4.If a + b = 23 and ab = 132, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 51 × 49.
6. 6.Find the value of x² − 2xy + y² when x = 5 and y = 1.
7. 7.Use (a + b)² = a² + 2ab + b² to find 76².
8. 8.Use (a − b)² = a² − 2ab + b² to find 76².
9. 9.Use a² − b² = (a + b)(a − b) to find 90² − 55².
10. 10.If a − b = 2 and ab = 24, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 98².
12. 12.If a − b = 1 and ab = 42, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 79².
14. 14.Find the value of x² − 2xy + y² when x = 3 and y = 1.
15. 15.Use (a + b)(a − b) = a² − b² to find 57 × 43.
16. 16.Use (a + b)² = a² + 2ab + b² to find 93².
17. 17.Use (a + b)² = a² + 2ab + b² to find 68².
18. 18.Use (a − b)² = a² − 2ab + b² to find 12².
19. 19.Use (a + b)² = a² + 2ab + b² to find 18².
20. 20.Use (a − b)² = a² − 2ab + b² to find 39².
21. 21.Find the value of x² − y² when x = 4 and y = 3.
22. 22.Find the value of x² + 2xy + y² when x = 9 and y = 4.
23. 23.Find the value of x² + 2xy + y² when x = 12 and y = 1.
24. 24.If a + b = 16 and ab = 60, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 83 × 77.
26. 26.Use (a + b)² = a² + 2ab + b² to find 81².
27. 27.Use a² − b² = (a + b)(a − b) to find 31² − 4².
28. 28.Use a² − b² = (a + b)(a − b) to find 22² − 4².
29. 29.Use a² − b² = (a + b)(a − b) to find 57² − 18².
30. 30.Use (a + b)² = a² + 2ab + b² to find 103².
31. 31.If a + b = 11 and ab = 30, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 76 × 64.
33. 33.Use (a − b)² = a² − 2ab + b² to find 53².
34. 34.Find the value of x² − y² when x = 4 and y = 2.
35. 35.Use a² − b² = (a + b)(a − b) to find 95² − 86².
36. 36.Use (a + b)² = a² + 2ab + b² to find 13².
37. 37.Find the value of x² − 2xy + y² when x = 10 and y = 8.
38. 38.Use (a − b)² = a² − 2ab + b² to find 83².
39. 39.Use (a + b)(a − b) = a² − b² to find 43 × 37.
40. 40.Use a² − b² = (a + b)(a − b) to find 21² − 13².

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