Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 724 · 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 21².
2. 2.Use a² − b² = (a + b)(a − b) to find 59² − 32².
3. 3.Use (a + b)(a − b) = a² − b² to find 71 × 69.
4. 4.Use a² − b² = (a + b)(a − b) to find 65² − 36².
5. 5.Use (a + b)(a − b) = a² − b² to find 44 × 36.
6. 6.Use a² − b² = (a + b)(a − b) to find 94² − 19².
7. 7.Find the value of x² − y² when x = 15 and y = 6.
8. 8.If a − b = 7 and ab = 8, what is a² + b²?
9. 9.If a − b = 8 and ab = 33, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 19².
11. 11.Find the value of x² − y² when x = 7 and y = 2.
12. 12.Use (a + b)² = a² + 2ab + b² to find 91².
13. 13.If a − b = 1 and ab = 56, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 47² − 9².
15. 15.Use a² − b² = (a + b)(a − b) to find 82² − 24².
16. 16.Use a² − b² = (a + b)(a − b) to find 43² − 15².
17. 17.If a + b = 14 and ab = 33, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 83².
19. 19.If a − b = 5 and ab = 6, what is a² + b²?
20. 20.If a + b = 12 and ab = 32, what is a² + b²?
21. 21.Find the value of x² − y² when x = 6 and y = 2.
22. 22.If a + b = 14 and ab = 48, what is a² + b²?
23. 23.Find the value of x² − 2xy + y² when x = 11 and y = 7.
24. 24.Use a² − b² = (a + b)(a − b) to find 26² − 11².
25. 25.Use (a + b)² = a² + 2ab + b² to find 86².
26. 26.Use (a + b)² = a² + 2ab + b² to find 63².
27. 27.Use (a + b)(a − b) = a² − b² to find 64 × 56.
28. 28.Find the value of x² + 2xy + y² when x = 14 and y = 9.
29. 29.Use (a − b)² = a² − 2ab + b² to find 75².
30. 30.Use (a + b)² = a² + 2ab + b² to find 22².
31. 31.Use (a + b)(a − b) = a² − b² to find 56 × 44.
32. 32.Find the value of x² − y² when x = 11 and y = 8.
33. 33.Use a² − b² = (a + b)(a − b) to find 40² − 19².
34. 34.Use (a + b)² = a² + 2ab + b² to find 109².
35. 35.Use (a + b)² = a² + 2ab + b² to find 38².
36. 36.If a − b = 4 and ab = 60, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 15².
38. 38.Find the value of x² − y² when x = 3 and y = 1.
39. 39.Use (a + b)² = a² + 2ab + b² to find 28².
40. 40.Use (a + b)(a − b) = a² − b² to find 31 × 29.

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