Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 848 · 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.Use (a − b)² = a² − 2ab + b² to find 83².
2. 2.Find the value of x² − y² when x = 10 and y = 2.
3. 3.Use (a − b)² = a² − 2ab + b² to find 73².
4. 4.Use (a + b)(a − b) = a² − b² to find 48 × 32.
5. 5.Use (a − b)² = a² − 2ab + b² to find 97².
6. 6.Use (a + b)² = a² + 2ab + b² to find 57².
7. 7.Use (a − b)² = a² − 2ab + b² to find 72².
8. 8.If a + b = 10 and ab = 9, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 82².
10. 10.If a + b = 18 and ab = 77, what is a² + b²?
11. 11.Find the value of x² + 2xy + y² when x = 4 and y = 3.
12. 12.Use a² − b² = (a + b)(a − b) to find 23² − 8².
13. 13.Use (a − b)² = a² − 2ab + b² to find 27².
14. 14.Use (a + b)² = a² + 2ab + b² to find 91².
15. 15.Use (a + b)² = a² + 2ab + b² to find 32².
16. 16.Use (a + b)(a − b) = a² − b² to find 43 × 37.
17. 17.Use (a + b)² = a² + 2ab + b² to find 94².
18. 18.Use (a + b)(a − b) = a² − b² to find 71 × 69.
19. 19.Use (a + b)² = a² + 2ab + b² to find 37².
20. 20.Use (a + b)² = a² + 2ab + b² to find 41².
21. 21.Use (a + b)² = a² + 2ab + b² to find 76².
22. 22.Use (a − b)² = a² − 2ab + b² to find 18².
23. 23.Use (a + b)² = a² + 2ab + b² to find 97².
24. 24.Use (a + b)(a − b) = a² − b² to find 93 × 87.
25. 25.If a + b = 20 and ab = 99, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 54² − 44².
27. 27.Use (a + b)² = a² + 2ab + b² to find 64².
28. 28.Use a² − b² = (a + b)(a − b) to find 27² − 20².
29. 29.Find the value of x² + 2xy + y² when x = 4 and y = 2.
30. 30.Use (a + b)² = a² + 2ab + b² to find 12².
31. 31.Use (a + b)(a − b) = a² − b² to find 105 × 95.
32. 32.Use a² − b² = (a + b)(a − b) to find 54² − 29².
33. 33.If a − b = 1 and ab = 6, what is a² + b²?
34. 34.Find the value of x² − 2xy + y² when x = 5 and y = 1.
35. 35.If a − b = 3 and ab = 18, what is a² + b²?
36. 36.If a + b = 13 and ab = 36, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 46².
38. 38.Use (a − b)² = a² − 2ab + b² to find 45².
39. 39.Use (a + b)(a − b) = a² − b² to find 91 × 89.
40. 40.If a − b = 4 and ab = 45, what is a² + b²?

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