Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 965 · 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)(a − b) = a² − b² to find 107 × 93.
2. 2.Use (a − b)² = a² − 2ab + b² to find 46².
3. 3.Use (a − b)² = a² − 2ab + b² to find 36².
4. 4.If a + b = 3 and ab = 2, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 21² − 11².
6. 6.If a − b = 1 and ab = 2, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 22².
8. 8.Use (a + b)(a − b) = a² − b² to find 33 × 27.
9. 9.Use (a + b)² = a² + 2ab + b² to find 52².
10. 10.Use (a + b)² = a² + 2ab + b² to find 95².
11. 11.Use a² − b² = (a + b)(a − b) to find 56² − 1².
12. 12.Find the value of x² + 2xy + y² when x = 5 and y = 3.
13. 13.Use a² − b² = (a + b)(a − b) to find 84² − 18².
14. 14.Use (a + b)(a − b) = a² − b² to find 62 × 58.
15. 15.Use (a − b)² = a² − 2ab + b² to find 32².
16. 16.Use (a + b)(a − b) = a² − b² to find 37 × 23.
17. 17.Use a² − b² = (a + b)(a − b) to find 86² − 33².
18. 18.Use (a + b)(a − b) = a² − b² to find 101 × 99.
19. 19.Find the value of x² − 2xy + y² when x = 4 and y = 3.
20. 20.If a − b = 10 and ab = 11, what is a² + b²?
21. 21.Find the value of x² − 2xy + y² when x = 11 and y = 4.
22. 22.Use (a − b)² = a² − 2ab + b² to find 86².
23. 23.Find the value of x² − y² when x = 10 and y = 5.
24. 24.If a − b = 6 and ab = 27, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 17².
26. 26.Use a² − b² = (a + b)(a − b) to find 57² − 15².
27. 27.Find the value of x² − y² when x = 12 and y = 5.
28. 28.Find the value of x² − y² when x = 5 and y = 4.
29. 29.If a + b = 8 and ab = 12, what is a² + b²?
30. 30.Find the value of x² − y² when x = 4 and y = 3.
31. 31.Use (a + b)(a − b) = a² − b² to find 31 × 29.
32. 32.Use (a − b)² = a² − 2ab + b² to find 34².
33. 33.Use (a + b)² = a² + 2ab + b² to find 104².
34. 34.Use (a + b)² = a² + 2ab + b² to find 13².
35. 35.Use (a − b)² = a² − 2ab + b² to find 71².
36. 36.Find the value of x² − 2xy + y² when x = 10 and y = 3.
37. 37.Use (a − b)² = a² − 2ab + b² to find 76².
38. 38.Use (a − b)² = a² − 2ab + b² to find 98².
39. 39.Use (a − b)² = a² − 2ab + b² to find 93².
40. 40.Use (a + b)² = a² + 2ab + b² to find 14².

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