Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 855 · 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 (a − b)² = a² − 2ab + b² to find 19².
2. 2.Use (a − b)² = a² − 2ab + b² to find 64².
3. 3.Use (a + b)² = a² + 2ab + b² to find 61².
4. 4.Use (a + b)(a − b) = a² − b² to find 84 × 76.
5. 5.Use (a + b)² = a² + 2ab + b² to find 82².
6. 6.Use (a − b)² = a² − 2ab + b² to find 96².
7. 7.Use a² − b² = (a + b)(a − b) to find 82² − 77².
8. 8.Use (a − b)² = a² − 2ab + b² to find 71².
9. 9.Use (a − b)² = a² − 2ab + b² to find 48².
10. 10.Find the value of x² − y² when x = 4 and y = 3.
11. 11.Use (a − b)² = a² − 2ab + b² to find 87².
12. 12.Use (a + b)(a − b) = a² − b² to find 65 × 55.
13. 13.Use a² − b² = (a + b)(a − b) to find 28² − 26².
14. 14.Use a² − b² = (a + b)(a − b) to find 32² − 24².
15. 15.Use (a − b)² = a² − 2ab + b² to find 93².
16. 16.Use (a + b)² = a² + 2ab + b² to find 16².
17. 17.Use a² − b² = (a + b)(a − b) to find 78² − 35².
18. 18.If a − b = 6 and ab = 7, what is a² + b²?
19. 19.If a − b = 4 and ab = 45, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 53².
21. 21.Find the value of x² − y² when x = 11 and y = 2.
22. 22.If a + b = 15 and ab = 36, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 27².
24. 24.Use (a + b)(a − b) = a² − b² to find 47 × 33.
25. 25.Use (a − b)² = a² − 2ab + b² to find 12².
26. 26.Use (a − b)² = a² − 2ab + b² to find 91².
27. 27.Use (a + b)² = a² + 2ab + b² to find 25².
28. 28.Use (a + b)² = a² + 2ab + b² to find 81².
29. 29.Use (a + b)² = a² + 2ab + b² to find 17².
30. 30.Use (a + b)² = a² + 2ab + b² to find 14².
31. 31.If a + b = 3 and ab = 2, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 24² − 2².
33. 33.Use (a + b)² = a² + 2ab + b² to find 23².
34. 34.Use (a − b)² = a² − 2ab + b² to find 39².
35. 35.If a + b = 17 and ab = 72, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 16².
37. 37.Find the value of x² − y² when x = 5 and y = 1.
38. 38.Find the value of x² + 2xy + y² when x = 11 and y = 1.
39. 39.If a − b = 3 and ab = 4, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 67².

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