Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 672 · 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 = 2 and ab = 48, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 101².
3. 3.Use (a + b)(a − b) = a² − b² to find 75 × 65.
4. 4.Use (a + b)² = a² + 2ab + b² to find 81².
5. 5.Use (a + b)(a − b) = a² − b² to find 81 × 79.
6. 6.Find the value of x² − y² when x = 6 and y = 1.
7. 7.Use a² − b² = (a + b)(a − b) to find 88² − 14².
8. 8.If a + b = 7 and ab = 6, what is a² + b²?
9. 9.If a − b = 7 and ab = 60, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 22 × 18.
11. 11.Use a² − b² = (a + b)(a − b) to find 32² − 16².
12. 12.Use (a − b)² = a² − 2ab + b² to find 19².
13. 13.If a − b = 4 and ab = 21, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 91².
15. 15.Use (a − b)² = a² − 2ab + b² to find 57².
16. 16.Use a² − b² = (a + b)(a − b) to find 40² − 17².
17. 17.Use (a − b)² = a² − 2ab + b² to find 96².
18. 18.Find the value of x² − 2xy + y² when x = 6 and y = 3.
19. 19.Find the value of x² − 2xy + y² when x = 3 and y = 1.
20. 20.Use a² − b² = (a + b)(a − b) to find 92² − 16².
21. 21.Use (a − b)² = a² − 2ab + b² to find 17².
22. 22.Use (a − b)² = a² − 2ab + b² to find 43².
23. 23.Use (a − b)² = a² − 2ab + b² to find 58².
24. 24.Find the value of x² − 2xy + y² when x = 12 and y = 1.
25. 25.Use a² − b² = (a + b)(a − b) to find 26² − 24².
26. 26.Use (a + b)(a − b) = a² − b² to find 42 × 38.
27. 27.Use (a + b)² = a² + 2ab + b² to find 12².
28. 28.Use a² − b² = (a + b)(a − b) to find 59² − 35².
29. 29.Find the value of x² − y² when x = 3 and y = 1.
30. 30.Use (a − b)² = a² − 2ab + b² to find 21².
31. 31.Use (a − b)² = a² − 2ab + b² to find 45².
32. 32.If a + b = 14 and ab = 45, what is a² + b²?
33. 33.If a + b = 6 and ab = 5, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 83².
35. 35.Use (a + b)(a − b) = a² − b² to find 32 × 28.
36. 36.Use (a + b)(a − b) = a² − b² to find 71 × 69.
37. 37.If a + b = 12 and ab = 11, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 63² − 55².
39. 39.Use (a − b)² = a² − 2ab + b² to find 25².
40. 40.Use (a + b)(a − b) = a² − b² to find 53 × 47.

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