Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 637 · 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 = 1 and ab = 6, what is a² + b²?
2. 2.If a + b = 22 and ab = 120, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 59².
4. 4.Use (a + b)² = a² + 2ab + b² to find 85².
5. 5.Use a² − b² = (a + b)(a − b) to find 54² − 12².
6. 6.Use (a + b)² = a² + 2ab + b² to find 73².
7. 7.Use a² − b² = (a + b)(a − b) to find 65² − 57².
8. 8.Use a² − b² = (a + b)(a − b) to find 43² − 35².
9. 9.Use (a + b)(a − b) = a² − b² to find 81 × 79.
10. 10.Use (a + b)² = a² + 2ab + b² to find 82².
11. 11.If a + b = 14 and ab = 48, what is a² + b²?
12. 12.If a + b = 18 and ab = 72, what is a² + b²?
13. 13.Find the value of x² − 2xy + y² when x = 13 and y = 5.
14. 14.Use (a + b)(a − b) = a² − b² to find 36 × 24.
15. 15.If a + b = 8 and ab = 15, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 56² − 7².
17. 17.Use (a + b)² = a² + 2ab + b² to find 78².
18. 18.If a + b = 9 and ab = 14, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 22² − 7².
20. 20.Use (a + b)² = a² + 2ab + b² to find 63².
21. 21.Use (a + b)² = a² + 2ab + b² to find 53².
22. 22.Use (a − b)² = a² − 2ab + b² to find 36².
23. 23.Use (a + b)² = a² + 2ab + b² to find 23².
24. 24.Use (a + b)(a − b) = a² − b² to find 41 × 39.
25. 25.Use a² − b² = (a + b)(a − b) to find 98² − 16².
26. 26.If a − b = 5 and ab = 6, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 38² − 37².
28. 28.If a + b = 14 and ab = 40, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 11².
30. 30.Use (a − b)² = a² − 2ab + b² to find 15².
31. 31.Find the value of x² − 2xy + y² when x = 8 and y = 5.
32. 32.Use a² − b² = (a + b)(a − b) to find 60² − 7².
33. 33.Use (a − b)² = a² − 2ab + b² to find 38².
34. 34.If a + b = 6 and ab = 8, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 89² − 71².
36. 36.Use a² − b² = (a + b)(a − b) to find 98² − 73².
37. 37.Use a² − b² = (a + b)(a − b) to find 32² − 3².
38. 38.If a − b = 2 and ab = 3, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 51² − 42².
40. 40.Use (a + b)(a − b) = a² − b² to find 88 × 72.

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