Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 331 · 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.If a − b = 2 and ab = 3, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 37 × 23.
3. 3.Use (a + b)² = a² + 2ab + b² to find 82².
4. 4.Find the value of x² − y² when x = 6 and y = 3.
5. 5.Use (a + b)² = a² + 2ab + b² to find 15².
6. 6.Use (a + b)² = a² + 2ab + b² to find 62².
7. 7.Use (a + b)² = a² + 2ab + b² to find 23².
8. 8.Find the value of x² + 2xy + y² when x = 6 and y = 1.
9. 9.Use (a + b)² = a² + 2ab + b² to find 22².
10. 10.If a + b = 13 and ab = 22, what is a² + b²?
11. 11.Find the value of x² − 2xy + y² when x = 8 and y = 5.
12. 12.Use a² − b² = (a + b)(a − b) to find 20² − 9².
13. 13.Find the value of x² − y² when x = 6 and y = 2.
14. 14.Use (a − b)² = a² − 2ab + b² to find 89².
15. 15.Use (a + b)² = a² + 2ab + b² to find 73².
16. 16.Use (a + b)² = a² + 2ab + b² to find 83².
17. 17.Find the value of x² + 2xy + y² when x = 5 and y = 2.
18. 18.If a − b = 6 and ab = 16, what is a² + b²?
19. 19.Find the value of x² − 2xy + y² when x = 5 and y = 2.
20. 20.Use a² − b² = (a + b)(a − b) to find 98² − 14².
21. 21.Use (a − b)² = a² − 2ab + b² to find 98².
22. 22.Use (a − b)² = a² − 2ab + b² to find 91².
23. 23.Find the value of x² + 2xy + y² when x = 12 and y = 9.
24. 24.Use (a + b)² = a² + 2ab + b² to find 26².
25. 25.Use (a + b)(a − b) = a² − b² to find 67 × 53.
26. 26.Use a² − b² = (a + b)(a − b) to find 48² − 40².
27. 27.Use (a + b)² = a² + 2ab + b² to find 95².
28. 28.Use (a − b)² = a² − 2ab + b² to find 45².
29. 29.Use (a + b)(a − b) = a² − b² to find 102 × 98.
30. 30.Find the value of x² − 2xy + y² when x = 14 and y = 7.
31. 31.If a − b = 1 and ab = 20, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 21 × 19.
33. 33.If a − b = 4 and ab = 5, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 14².
35. 35.If a + b = 4 and ab = 3, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 83² − 43².
37. 37.Use (a + b)² = a² + 2ab + b² to find 79².
38. 38.Use (a − b)² = a² − 2ab + b² to find 95².
39. 39.Use (a + b)² = a² + 2ab + b² to find 93².
40. 40.Use (a + b)(a − b) = a² − b² to find 103 × 97.

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