Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 432 · 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 92².
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 − 24².
4. 4.Find the value of x² − y² when x = 9 and y = 5.
5. 5.Use (a + b)(a − b) = a² − b² to find 74 × 66.
6. 6.If a + b = 5 and ab = 6, what is a² + b²?
7. 7.Find the value of x² − 2xy + y² when x = 4 and y = 3.
8. 8.Find the value of x² − y² when x = 10 and y = 1.
9. 9.Use (a − b)² = a² − 2ab + b² to find 73².
10. 10.Use (a + b)² = a² + 2ab + b² to find 84².
11. 11.Find the value of x² + 2xy + y² when x = 6 and y = 5.
12. 12.Use (a − b)² = a² − 2ab + b² to find 64².
13. 13.Use (a + b)² = a² + 2ab + b² to find 59².
14. 14.Use (a + b)² = a² + 2ab + b² to find 85².
15. 15.Use (a + b)² = a² + 2ab + b² to find 108².
16. 16.Use (a − b)² = a² − 2ab + b² to find 83².
17. 17.Use (a + b)(a − b) = a² − b² to find 69 × 51.
18. 18.Use (a + b)(a − b) = a² − b² to find 51 × 49.
19. 19.Find the value of x² + 2xy + y² when x = 11 and y = 6.
20. 20.Use a² − b² = (a + b)(a − b) to find 43² − 32².
21. 21.Use (a − b)² = a² − 2ab + b² to find 97².
22. 22.Use (a − b)² = a² − 2ab + b² to find 32².
23. 23.Use (a − b)² = a² − 2ab + b² to find 24².
24. 24.Use a² − b² = (a + b)(a − b) to find 45² − 15².
25. 25.Use (a + b)(a − b) = a² − b² to find 53 × 47.
26. 26.Use a² − b² = (a + b)(a − b) to find 33² − 8².
27. 27.Use (a + b)(a − b) = a² − b² to find 103 × 97.
28. 28.Find the value of x² − y² when x = 12 and y = 5.
29. 29.Use (a − b)² = a² − 2ab + b² to find 53².
30. 30.If a + b = 12 and ab = 20, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 58² − 20².
32. 32.Use (a − b)² = a² − 2ab + b² to find 88².
33. 33.Use (a − b)² = a² − 2ab + b² to find 19².
34. 34.Find the value of x² + 2xy + y² when x = 4 and y = 3.
35. 35.If a − b = 3 and ab = 28, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 102 × 98.
37. 37.Use (a + b)² = a² + 2ab + b² to find 103².
38. 38.Use a² − b² = (a + b)(a − b) to find 26² − 21².
39. 39.Use a² − b² = (a + b)(a − b) to find 77² − 8².
40. 40.If a − b = 2 and ab = 3, what is a² + b²?

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