Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 104 · 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 = 10 and ab = 24, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 103 × 97.
3. 3.Find the value of x² − y² when x = 11 and y = 6.
4. 4.Use (a − b)² = a² − 2ab + b² to find 35².
5. 5.Find the value of x² − 2xy + y² when x = 7 and y = 3.
6. 6.If a − b = 3 and ab = 10, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 99 × 81.
8. 8.Use (a + b)(a − b) = a² − b² to find 104 × 96.
9. 9.Use a² − b² = (a + b)(a − b) to find 42² − 34².
10. 10.Find the value of x² + 2xy + y² when x = 9 and y = 8.
11. 11.Use a² − b² = (a + b)(a − b) to find 96² − 79².
12. 12.Use (a − b)² = a² − 2ab + b² to find 37².
13. 13.If a − b = 2 and ab = 120, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 96² − 36².
15. 15.Use a² − b² = (a + b)(a − b) to find 31² − 22².
16. 16.Use (a + b)² = a² + 2ab + b² to find 24².
17. 17.Use (a − b)² = a² − 2ab + b² to find 73².
18. 18.Use a² − b² = (a + b)(a − b) to find 23² − 21².
19. 19.Use (a − b)² = a² − 2ab + b² to find 91².
20. 20.Use (a − b)² = a² − 2ab + b² to find 17².
21. 21.Use (a − b)² = a² − 2ab + b² to find 55².
22. 22.Use (a + b)(a − b) = a² − b² to find 61 × 59.
23. 23.Find the value of x² + 2xy + y² when x = 15 and y = 4.
24. 24.Use (a + b)² = a² + 2ab + b² to find 102².
25. 25.Use (a + b)(a − b) = a² − b² to find 71 × 69.
26. 26.Use (a − b)² = a² − 2ab + b² to find 22².
27. 27.If a + b = 3 and ab = 2, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 32² − 13².
29. 29.Use a² − b² = (a + b)(a − b) to find 54² − 30².
30. 30.Find the value of x² + 2xy + y² when x = 10 and y = 5.
31. 31.Use a² − b² = (a + b)(a − b) to find 55² − 34².
32. 32.Find the value of x² + 2xy + y² when x = 5 and y = 4.
33. 33.If a + b = 16 and ab = 55, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 65².
35. 35.Use (a + b)(a − b) = a² − b² to find 98 × 82.
36. 36.Use (a − b)² = a² − 2ab + b² to find 69².
37. 37.Use a² − b² = (a + b)(a − b) to find 42² − 6².
38. 38.Use (a + b)(a − b) = a² − b² to find 79 × 61.
39. 39.Use (a + b)(a − b) = a² − b² to find 109 × 91.
40. 40.Use (a − b)² = a² − 2ab + b² to find 59².

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