Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 867 · 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 a² − b² = (a + b)(a − b) to find 97² − 66².
2. 2.Use (a − b)² = a² − 2ab + b² to find 88².
3. 3.Use (a − b)² = a² − 2ab + b² to find 52².
4. 4.If a + b = 10 and ab = 24, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 26².
6. 6.Use (a + b)² = a² + 2ab + b² to find 93².
7. 7.Use (a + b)(a − b) = a² − b² to find 87 × 73.
8. 8.Use (a − b)² = a² − 2ab + b² to find 17².
9. 9.Use (a + b)² = a² + 2ab + b² to find 17².
10. 10.If a − b = 2 and ab = 120, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 98² − 57².
12. 12.Use a² − b² = (a + b)(a − b) to find 33² − 9².
13. 13.Use (a + b)² = a² + 2ab + b² to find 22².
14. 14.If a + b = 11 and ab = 10, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 84².
16. 16.If a − b = 7 and ab = 60, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 46 × 34.
18. 18.Use (a − b)² = a² − 2ab + b² to find 32².
19. 19.Use (a + b)² = a² + 2ab + b² to find 38².
20. 20.If a − b = 3 and ab = 40, what is a² + b²?
21. 21.Find the value of x² + 2xy + y² when x = 10 and y = 3.
22. 22.Use (a − b)² = a² − 2ab + b² to find 67².
23. 23.Find the value of x² − 2xy + y² when x = 5 and y = 3.
24. 24.Use (a − b)² = a² − 2ab + b² to find 87².
25. 25.Use (a − b)² = a² − 2ab + b² to find 28².
26. 26.Use a² − b² = (a + b)(a − b) to find 93² − 22².
27. 27.Find the value of x² + 2xy + y² when x = 11 and y = 8.
28. 28.If a − b = 5 and ab = 36, what is a² + b²?
29. 29.Find the value of x² + 2xy + y² when x = 6 and y = 5.
30. 30.Use (a − b)² = a² − 2ab + b² to find 57².
31. 31.Use (a + b)(a − b) = a² − b² to find 52 × 48.
32. 32.If a + b = 20 and ab = 96, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 77².
34. 34.Use a² − b² = (a + b)(a − b) to find 47² − 12².
35. 35.Use (a + b)² = a² + 2ab + b² to find 94².
36. 36.Use (a + b)(a − b) = a² − b² to find 72 × 68.
37. 37.Use (a − b)² = a² − 2ab + b² to find 13².
38. 38.Find the value of x² + 2xy + y² when x = 12 and y = 7.
39. 39.Use (a + b)² = a² + 2ab + b² to find 89².
40. 40.Use (a + b)² = a² + 2ab + b² to find 16².

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