Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 891 · 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 73² − 16².
2. 2.If a + b = 7 and ab = 10, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 34² − 3².
4. 4.Use (a + b)(a − b) = a² − b² to find 61 × 59.
5. 5.Use a² − b² = (a + b)(a − b) to find 95² − 72².
6. 6.Use (a + b)(a − b) = a² − b² to find 58 × 42.
7. 7.Use a² − b² = (a + b)(a − b) to find 32² − 4².
8. 8.Use (a + b)(a − b) = a² − b² to find 73 × 67.
9. 9.Use (a − b)² = a² − 2ab + b² to find 65².
10. 10.Find the value of x² + 2xy + y² when x = 13 and y = 8.
11. 11.Use a² − b² = (a + b)(a − b) to find 46² − 1².
12. 12.Use (a + b)² = a² + 2ab + b² to find 22².
13. 13.Use (a + b)(a − b) = a² − b² to find 45 × 35.
14. 14.Use a² − b² = (a + b)(a − b) to find 72² − 1².
15. 15.Use (a + b)(a − b) = a² − b² to find 51 × 49.
16. 16.Use (a + b)(a − b) = a² − b² to find 31 × 29.
17. 17.Use a² − b² = (a + b)(a − b) to find 64² − 1².
18. 18.Use a² − b² = (a + b)(a − b) to find 65² − 48².
19. 19.If a − b = 2 and ab = 3, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 57 × 43.
21. 21.Use (a − b)² = a² − 2ab + b² to find 59².
22. 22.Find the value of x² − y² when x = 15 and y = 1.
23. 23.Use (a − b)² = a² − 2ab + b² to find 26².
24. 24.Use (a + b)² = a² + 2ab + b² to find 71².
25. 25.Use a² − b² = (a + b)(a − b) to find 76² − 16².
26. 26.Use (a + b)² = a² + 2ab + b² to find 35².
27. 27.Find the value of x² − y² when x = 10 and y = 8.
28. 28.If a + b = 22 and ab = 120, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 11².
30. 30.If a + b = 7 and ab = 12, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 68 × 52.
32. 32.Use a² − b² = (a + b)(a − b) to find 30² − 28².
33. 33.If a + b = 12 and ab = 32, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 82².
35. 35.Use a² − b² = (a + b)(a − b) to find 82² − 44².
36. 36.Find the value of x² + 2xy + y² when x = 10 and y = 9.
37. 37.Use a² − b² = (a + b)(a − b) to find 99² − 31².
38. 38.If a + b = 10 and ab = 16, what is a² + b²?
39. 39.Find the value of x² − y² when x = 4 and y = 2.
40. 40.Use (a − b)² = a² − 2ab + b² to find 94².

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