Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 48 · 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.Find the value of x² − 2xy + y² when x = 9 and y = 5.
2. 2.Use a² − b² = (a + b)(a − b) to find 33² − 22².
3. 3.Find the value of x² − y² when x = 11 and y = 10.
4. 4.Use a² − b² = (a + b)(a − b) to find 80² − 17².
5. 5.Use a² − b² = (a + b)(a − b) to find 45² − 37².
6. 6.Use (a + b)² = a² + 2ab + b² to find 42².
7. 7.If a − b = 4 and ab = 60, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 51².
9. 9.Use (a + b)(a − b) = a² − b² to find 102 × 98.
10. 10.Use (a + b)² = a² + 2ab + b² to find 44².
11. 11.Use (a + b)² = a² + 2ab + b² to find 22².
12. 12.Use (a − b)² = a² − 2ab + b² to find 89².
13. 13.Use (a + b)(a − b) = a² − b² to find 56 × 44.
14. 14.If a − b = 4 and ab = 96, what is a² + b²?
15. 15.If a − b = 7 and ab = 30, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 68².
17. 17.Use (a − b)² = a² − 2ab + b² to find 15².
18. 18.Use (a − b)² = a² − 2ab + b² to find 26².
19. 19.Use (a − b)² = a² − 2ab + b² to find 22².
20. 20.Use (a + b)(a − b) = a² − b² to find 59 × 41.
21. 21.Use a² − b² = (a + b)(a − b) to find 20² − 14².
22. 22.Use a² − b² = (a + b)(a − b) to find 31² − 3².
23. 23.Use (a + b)² = a² + 2ab + b² to find 63².
24. 24.If a − b = 4 and ab = 21, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 44 × 36.
26. 26.Use (a + b)² = a² + 2ab + b² to find 54².
27. 27.Use (a + b)(a − b) = a² − b² to find 25 × 15.
28. 28.Use a² − b² = (a + b)(a − b) to find 29² − 6².
29. 29.If a − b = 5 and ab = 14, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 32 × 28.
31. 31.Use (a + b)² = a² + 2ab + b² to find 49².
32. 32.Use (a + b)² = a² + 2ab + b² to find 107².
33. 33.Use (a − b)² = a² − 2ab + b² to find 85².
34. 34.Find the value of x² + 2xy + y² when x = 4 and y = 3.
35. 35.Use (a + b)(a − b) = a² − b² to find 55 × 45.
36. 36.Use (a + b)² = a² + 2ab + b² to find 19².
37. 37.Find the value of x² − y² when x = 5 and y = 4.
38. 38.Use (a − b)² = a² − 2ab + b² to find 41².
39. 39.Use a² − b² = (a + b)(a − b) to find 66² − 46².
40. 40.Use a² − b² = (a + b)(a − b) to find 26² − 12².

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