Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 74 · 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 a² − b² = (a + b)(a − b) to find 28² − 2².
2. 2.If a + b = 8 and ab = 15, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 43 × 37.
4. 4.If a + b = 13 and ab = 40, what is a² + b²?
5. 5.Find the value of x² + 2xy + y² when x = 9 and y = 7.
6. 6.Use a² − b² = (a + b)(a − b) to find 46² − 26².
7. 7.Use a² − b² = (a + b)(a − b) to find 41² − 10².
8. 8.Use (a − b)² = a² − 2ab + b² to find 29².
9. 9.Find the value of x² + 2xy + y² when x = 11 and y = 3.
10. 10.Use (a + b)² = a² + 2ab + b² to find 92².
11. 11.Use (a + b)² = a² + 2ab + b² to find 59².
12. 12.Use a² − b² = (a + b)(a − b) to find 89² − 27².
13. 13.If a + b = 7 and ab = 6, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 26² − 11².
15. 15.Use a² − b² = (a + b)(a − b) to find 47² − 31².
16. 16.Use a² − b² = (a + b)(a − b) to find 21² − 9².
17. 17.Use (a − b)² = a² − 2ab + b² to find 33².
18. 18.Find the value of x² − y² when x = 11 and y = 8.
19. 19.Use (a + b)(a − b) = a² − b² to find 71 × 69.
20. 20.Use a² − b² = (a + b)(a − b) to find 45² − 24².
21. 21.If a + b = 4 and ab = 3, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 35².
23. 23.If a + b = 8 and ab = 7, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 99 × 81.
25. 25.Use (a + b)(a − b) = a² − b² to find 78 × 62.
26. 26.Find the value of x² − y² when x = 7 and y = 4.
27. 27.Use (a − b)² = a² − 2ab + b² to find 38².
28. 28.If a + b = 19 and ab = 84, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 52².
30. 30.Use (a + b)² = a² + 2ab + b² to find 71².
31. 31.Find the value of x² − y² when x = 4 and y = 2.
32. 32.Use a² − b² = (a + b)(a − b) to find 23² − 10².
33. 33.Find the value of x² − y² when x = 3 and y = 1.
34. 34.Use (a − b)² = a² − 2ab + b² to find 52².
35. 35.Use (a + b)(a − b) = a² − b² to find 97 × 83.
36. 36.If a − b = 6 and ab = 27, what is a² + b²?
37. 37.If a − b = 7 and ab = 60, what is a² + b²?
38. 38.If a + b = 11 and ab = 30, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 31².
40. 40.If a − b = 6 and ab = 55, what is a² + b²?

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