Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 967 · 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 31 × 29.
2. 2.Find the value of x² − 2xy + y² when x = 4 and y = 3.
3. 3.Use (a + b)² = a² + 2ab + b² to find 45².
4. 4.Find the value of x² − 2xy + y² when x = 13 and y = 10.
5. 5.Find the value of x² − 2xy + y² when x = 5 and y = 2.
6. 6.Use (a − b)² = a² − 2ab + b² to find 62².
7. 7.Use (a + b)(a − b) = a² − b² to find 98 × 82.
8. 8.Use (a + b)² = a² + 2ab + b² to find 17².
9. 9.Find the value of x² + 2xy + y² when x = 15 and y = 1.
10. 10.If a − b = 1 and ab = 12, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 71².
12. 12.Use (a − b)² = a² − 2ab + b² to find 33².
13. 13.Use (a − b)² = a² − 2ab + b² to find 84².
14. 14.If a + b = 12 and ab = 32, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 27².
16. 16.If a + b = 12 and ab = 35, what is a² + b²?
17. 17.Find the value of x² − y² when x = 13 and y = 1.
18. 18.Use (a + b)² = a² + 2ab + b² to find 76².
19. 19.Use (a + b)(a − b) = a² − b² to find 51 × 49.
20. 20.Use (a − b)² = a² − 2ab + b² to find 98².
21. 21.Find the value of x² − 2xy + y² when x = 4 and y = 2.
22. 22.Use (a + b)² = a² + 2ab + b² to find 39².
23. 23.Use (a + b)² = a² + 2ab + b² to find 61².
24. 24.Use (a + b)² = a² + 2ab + b² to find 41².
25. 25.Use (a − b)² = a² − 2ab + b² to find 61².
26. 26.Use a² − b² = (a + b)(a − b) to find 49² − 22².
27. 27.Find the value of x² − 2xy + y² when x = 11 and y = 1.
28. 28.Use a² − b² = (a + b)(a − b) to find 26² − 11².
29. 29.Find the value of x² + 2xy + y² when x = 14 and y = 5.
30. 30.If a + b = 8 and ab = 12, what is a² + b²?
31. 31.Find the value of x² − 2xy + y² when x = 4 and y = 1.
32. 32.Use (a + b)(a − b) = a² − b² to find 48 × 32.
33. 33.Use (a + b)² = a² + 2ab + b² to find 62².
34. 34.Use (a + b)(a − b) = a² − b² to find 45 × 35.
35. 35.Use (a + b)(a − b) = a² − b² to find 55 × 45.
36. 36.Use (a + b)(a − b) = a² − b² to find 38 × 22.
37. 37.Use (a + b)(a − b) = a² − b² to find 89 × 71.
38. 38.If a − b = 3 and ab = 18, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 104².
40. 40.Use a² − b² = (a + b)(a − b) to find 23² − 18².

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