Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 386 · 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 41² − 30².
2. 2.If a + b = 3 and ab = 2, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 96² − 40².
4. 4.Use (a + b)² = a² + 2ab + b² to find 18².
5. 5.Use (a + b)² = a² + 2ab + b² to find 15².
6. 6.If a − b = 8 and ab = 20, what is a² + b²?
7. 7.If a − b = 1 and ab = 2, what is a² + b²?
8. 8.Find the value of x² − y² when x = 15 and y = 11.
9. 9.Use (a + b)² = a² + 2ab + b² to find 106².
10. 10.Use (a + b)² = a² + 2ab + b² to find 78².
11. 11.Use (a − b)² = a² − 2ab + b² to find 61².
12. 12.Use (a − b)² = a² − 2ab + b² to find 99².
13. 13.If a − b = 5 and ab = 14, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 60² − 32².
15. 15.Use (a + b)² = a² + 2ab + b² to find 84².
16. 16.Use a² − b² = (a + b)(a − b) to find 87² − 62².
17. 17.If a + b = 10 and ab = 16, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 96 × 84.
19. 19.Use (a + b)² = a² + 2ab + b² to find 104².
20. 20.Use a² − b² = (a + b)(a − b) to find 39² − 6².
21. 21.Use (a + b)² = a² + 2ab + b² to find 17².
22. 22.Use a² − b² = (a + b)(a − b) to find 42² − 34².
23. 23.If a + b = 4 and ab = 3, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 28².
25. 25.Use (a + b)² = a² + 2ab + b² to find 11².
26. 26.If a + b = 15 and ab = 56, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 94².
28. 28.Use a² − b² = (a + b)(a − b) to find 26² − 22².
29. 29.Use (a + b)² = a² + 2ab + b² to find 56².
30. 30.Find the value of x² − y² when x = 3 and y = 2.
31. 31.Find the value of x² − 2xy + y² when x = 14 and y = 10.
32. 32.Use (a + b)(a − b) = a² − b² to find 55 × 45.
33. 33.Use (a + b)(a − b) = a² − b² to find 79 × 61.
34. 34.Use (a + b)(a − b) = a² − b² to find 43 × 37.
35. 35.If a + b = 5 and ab = 4, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 12².
37. 37.Use a² − b² = (a + b)(a − b) to find 45² − 31².
38. 38.Use a² − b² = (a + b)(a − b) to find 23² − 11².
39. 39.Use (a − b)² = a² − 2ab + b² to find 35².
40. 40.Use (a − b)² = a² − 2ab + b² to find 34².

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