Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 360 · 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 36².
2. 2.Find the value of x² − 2xy + y² when x = 5 and y = 1.
3. 3.Find the value of x² − 2xy + y² when x = 6 and y = 1.
4. 4.Use (a − b)² = a² − 2ab + b² to find 21².
5. 5.Use (a + b)² = a² + 2ab + b² to find 91².
6. 6.Use (a + b)² = a² + 2ab + b² to find 66².
7. 7.Use (a + b)² = a² + 2ab + b² to find 58².
8. 8.Use a² − b² = (a + b)(a − b) to find 66² − 43².
9. 9.Use a² − b² = (a + b)(a − b) to find 81² − 1².
10. 10.Use a² − b² = (a + b)(a − b) to find 26² − 3².
11. 11.If a + b = 3 and ab = 2, what is a² + b²?
12. 12.If a + b = 4 and ab = 3, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 93² − 86².
14. 14.Use (a − b)² = a² − 2ab + b² to find 97².
15. 15.Use a² − b² = (a + b)(a − b) to find 27² − 9².
16. 16.Use (a + b)(a − b) = a² − b² to find 56 × 44.
17. 17.Find the value of x² − 2xy + y² when x = 8 and y = 6.
18. 18.Use (a − b)² = a² − 2ab + b² to find 15².
19. 19.Use (a − b)² = a² − 2ab + b² to find 22².
20. 20.Use a² − b² = (a + b)(a − b) to find 97² − 58².
21. 21.Use (a − b)² = a² − 2ab + b² to find 58².
22. 22.Use (a + b)(a − b) = a² − b² to find 44 × 36.
23. 23.Use a² − b² = (a + b)(a − b) to find 55² − 22².
24. 24.Find the value of x² − y² when x = 9 and y = 5.
25. 25.Use a² − b² = (a + b)(a − b) to find 40² − 3².
26. 26.Use a² − b² = (a + b)(a − b) to find 23² − 6².
27. 27.Use (a + b)² = a² + 2ab + b² to find 107².
28. 28.Use a² − b² = (a + b)(a − b) to find 95² − 13².
29. 29.If a − b = 1 and ab = 2, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 45².
31. 31.Use (a + b)(a − b) = a² − b² to find 104 × 96.
32. 32.Use a² − b² = (a + b)(a − b) to find 39² − 23².
33. 33.Use a² − b² = (a + b)(a − b) to find 62² − 37².
34. 34.Use a² − b² = (a + b)(a − b) to find 62² − 41².
35. 35.Use (a − b)² = a² − 2ab + b² to find 35².
36. 36.Use (a + b)² = a² + 2ab + b² to find 46².
37. 37.Use (a + b)(a − b) = a² − b² to find 26 × 14.
38. 38.Use (a + b)(a − b) = a² − b² to find 105 × 95.
39. 39.Use (a + b)(a − b) = a² − b² to find 37 × 23.
40. 40.If a − b = 6 and ab = 16, what is a² + b²?

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