Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 776 · 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 = 4 and ab = 5, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 91 × 89.
3. 3.Use a² − b² = (a + b)(a − b) to find 90² − 89².
4. 4.If a − b = 2 and ab = 3, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 53² − 36².
6. 6.Use (a − b)² = a² − 2ab + b² to find 85².
7. 7.Find the value of x² + 2xy + y² when x = 13 and y = 9.
8. 8.Use (a + b)² = a² + 2ab + b² to find 75².
9. 9.If a + b = 6 and ab = 5, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 65².
11. 11.Use (a + b)² = a² + 2ab + b² to find 106².
12. 12.If a + b = 9 and ab = 20, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 71².
14. 14.Use (a + b)² = a² + 2ab + b² to find 53².
15. 15.Find the value of x² + 2xy + y² when x = 3 and y = 1.
16. 16.Use (a − b)² = a² − 2ab + b² to find 68².
17. 17.Use (a + b)² = a² + 2ab + b² to find 27².
18. 18.Find the value of x² + 2xy + y² when x = 14 and y = 12.
19. 19.If a − b = 3 and ab = 4, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 99² − 15².
21. 21.Use a² − b² = (a + b)(a − b) to find 80² − 55².
22. 22.If a + b = 5 and ab = 6, what is a² + b²?
23. 23.Find the value of x² − 2xy + y² when x = 15 and y = 9.
24. 24.Use (a − b)² = a² − 2ab + b² to find 98².
25. 25.Use (a + b)(a − b) = a² − b² to find 95 × 85.
26. 26.Use (a + b)² = a² + 2ab + b² to find 41².
27. 27.Find the value of x² − 2xy + y² when x = 5 and y = 4.
28. 28.Use (a + b)² = a² + 2ab + b² to find 92².
29. 29.Use (a + b)² = a² + 2ab + b² to find 45².
30. 30.Find the value of x² + 2xy + y² when x = 4 and y = 1.
31. 31.Find the value of x² − y² when x = 11 and y = 7.
32. 32.Use (a − b)² = a² − 2ab + b² to find 45².
33. 33.If a + b = 18 and ab = 80, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 12².
35. 35.If a + b = 3 and ab = 2, what is a² + b²?
36. 36.If a + b = 9 and ab = 18, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 103 × 97.
38. 38.Use (a + b)² = a² + 2ab + b² to find 102².
39. 39.Use (a + b)(a − b) = a² − b² to find 32 × 28.
40. 40.Use (a + b)² = a² + 2ab + b² to find 61².

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