Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 694 · 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.Find the value of x² − y² when x = 11 and y = 1.
2. 2.Use a² − b² = (a + b)(a − b) to find 83² − 64².
3. 3.Find the value of x² − y² when x = 3 and y = 2.
4. 4.Use (a + b)² = a² + 2ab + b² to find 36².
5. 5.Use (a − b)² = a² − 2ab + b² to find 17².
6. 6.Use a² − b² = (a + b)(a − b) to find 60² − 44².
7. 7.Use (a + b)(a − b) = a² − b² to find 21 × 19.
8. 8.If a + b = 4 and ab = 3, what is a² + b²?
9. 9.If a + b = 15 and ab = 44, what is a² + b²?
10. 10.Find the value of x² − 2xy + y² when x = 10 and y = 8.
11. 11.Use a² − b² = (a + b)(a − b) to find 63² − 46².
12. 12.If a + b = 10 and ab = 24, what is a² + b²?
13. 13.Find the value of x² + 2xy + y² when x = 12 and y = 10.
14. 14.Find the value of x² − 2xy + y² when x = 12 and y = 4.
15. 15.Use (a − b)² = a² − 2ab + b² to find 19².
16. 16.Use a² − b² = (a + b)(a − b) to find 27² − 13².
17. 17.Use a² − b² = (a + b)(a − b) to find 88² − 42².
18. 18.If a − b = 1 and ab = 72, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 91².
20. 20.Use (a + b)(a − b) = a² − b² to find 72 × 68.
21. 21.Use (a + b)(a − b) = a² − b² to find 57 × 43.
22. 22.Use a² − b² = (a + b)(a − b) to find 45² − 39².
23. 23.If a + b = 5 and ab = 4, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 77 × 63.
25. 25.Use (a + b)(a − b) = a² − b² to find 35 × 25.
26. 26.Find the value of x² + 2xy + y² when x = 7 and y = 1.
27. 27.Use (a − b)² = a² − 2ab + b² to find 22².
28. 28.If a − b = 5 and ab = 84, what is a² + b²?
29. 29.Use a² − b² = (a + b)(a − b) to find 34² − 18².
30. 30.Use (a + b)² = a² + 2ab + b² to find 28².
31. 31.If a − b = 5 and ab = 6, what is a² + b²?
32. 32.If a + b = 10 and ab = 21, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 83².
34. 34.Use (a − b)² = a² − 2ab + b² to find 16².
35. 35.Use (a + b)(a − b) = a² − b² to find 25 × 15.
36. 36.Use (a − b)² = a² − 2ab + b² to find 87².
37. 37.Use (a + b)(a − b) = a² − b² to find 48 × 32.
38. 38.Use (a − b)² = a² − 2ab + b² to find 81².
39. 39.Use a² − b² = (a + b)(a − b) to find 52² − 25².
40. 40.Use (a − b)² = a² − 2ab + b² to find 57².

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