Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 563 · 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 65².
2. 2.Use (a + b)² = a² + 2ab + b² to find 55².
3. 3.Use (a − b)² = a² − 2ab + b² to find 18².
4. 4.Use (a + b)(a − b) = a² − b² to find 61 × 59.
5. 5.Use (a + b)² = a² + 2ab + b² to find 107².
6. 6.Find the value of x² + 2xy + y² when x = 7 and y = 5.
7. 7.Use (a + b)² = a² + 2ab + b² to find 48².
8. 8.If a − b = 7 and ab = 18, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 93².
10. 10.Use (a + b)² = a² + 2ab + b² to find 37².
11. 11.Use (a + b)² = a² + 2ab + b² to find 95².
12. 12.Use (a + b)² = a² + 2ab + b² to find 31².
13. 13.Use (a − b)² = a² − 2ab + b² to find 37².
14. 14.Use (a − b)² = a² − 2ab + b² to find 51².
15. 15.Use a² − b² = (a + b)(a − b) to find 20² − 6².
16. 16.If a + b = 15 and ab = 50, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 17².
18. 18.Use (a − b)² = a² − 2ab + b² to find 31².
19. 19.Use (a − b)² = a² − 2ab + b² to find 41².
20. 20.If a + b = 7 and ab = 12, what is a² + b²?
21. 21.If a + b = 16 and ab = 63, what is a² + b²?
22. 22.Find the value of x² − y² when x = 13 and y = 1.
23. 23.If a + b = 18 and ab = 72, what is a² + b²?
24. 24.If a − b = 7 and ab = 30, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 97².
26. 26.Find the value of x² + 2xy + y² when x = 5 and y = 3.
27. 27.Use (a + b)(a − b) = a² − b² to find 81 × 79.
28. 28.Find the value of x² − y² when x = 9 and y = 6.
29. 29.Use (a + b)² = a² + 2ab + b² to find 22².
30. 30.Use (a − b)² = a² − 2ab + b² to find 98².
31. 31.Find the value of x² − y² when x = 15 and y = 3.
32. 32.Use a² − b² = (a + b)(a − b) to find 40² − 29².
33. 33.Use (a − b)² = a² − 2ab + b² to find 95².
34. 34.If a + b = 12 and ab = 35, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 89².
36. 36.Use a² − b² = (a + b)(a − b) to find 29² − 15².
37. 37.Use a² − b² = (a + b)(a − b) to find 72² − 5².
38. 38.Use (a − b)² = a² − 2ab + b² to find 58².
39. 39.Use a² − b² = (a + b)(a − b) to find 87² − 28².
40. 40.Find the value of x² − y² when x = 6 and y = 5.

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