Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 414 · 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 58².
2. 2.Use (a + b)² = a² + 2ab + b² to find 42².
3. 3.Find the value of x² − y² when x = 11 and y = 9.
4. 4.Use (a + b)² = a² + 2ab + b² to find 29².
5. 5.Use (a − b)² = a² − 2ab + b² to find 88².
6. 6.Find the value of x² − 2xy + y² when x = 5 and y = 4.
7. 7.Use (a + b)² = a² + 2ab + b² to find 96².
8. 8.Use (a + b)² = a² + 2ab + b² to find 106².
9. 9.Use a² − b² = (a + b)(a − b) to find 57² − 24².
10. 10.Find the value of x² − y² when x = 3 and y = 2.
11. 11.Use (a − b)² = a² − 2ab + b² to find 99².
12. 12.Use (a − b)² = a² − 2ab + b² to find 85².
13. 13.Use (a + b)(a − b) = a² − b² to find 84 × 76.
14. 14.Use (a + b)(a − b) = a² − b² to find 58 × 42.
15. 15.Find the value of x² + 2xy + y² when x = 5 and y = 1.
16. 16.Use (a − b)² = a² − 2ab + b² to find 31².
17. 17.Use (a + b)(a − b) = a² − b² to find 102 × 98.
18. 18.Use a² − b² = (a + b)(a − b) to find 38² − 16².
19. 19.Use (a − b)² = a² − 2ab + b² to find 94².
20. 20.Use a² − b² = (a + b)(a − b) to find 39² − 34².
21. 21.Find the value of x² − 2xy + y² when x = 10 and y = 1.
22. 22.If a − b = 1 and ab = 2, what is a² + b²?
23. 23.If a + b = 19 and ab = 88, what is a² + b²?
24. 24.Find the value of x² − 2xy + y² when x = 14 and y = 11.
25. 25.Use (a + b)(a − b) = a² − b² to find 61 × 59.
26. 26.Use (a − b)² = a² − 2ab + b² to find 54².
27. 27.Use (a − b)² = a² − 2ab + b² to find 67².
28. 28.Use (a + b)² = a² + 2ab + b² to find 105².
29. 29.Use (a + b)(a − b) = a² − b² to find 91 × 89.
30. 30.Use (a + b)(a − b) = a² − b² to find 41 × 39.
31. 31.Find the value of x² − 2xy + y² when x = 6 and y = 4.
32. 32.Use a² − b² = (a + b)(a − b) to find 23² − 5².
33. 33.Use (a + b)² = a² + 2ab + b² to find 102².
34. 34.Use (a + b)² = a² + 2ab + b² to find 76².
35. 35.If a − b = 9 and ab = 10, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 97 × 83.
37. 37.Find the value of x² − 2xy + y² when x = 8 and y = 5.
38. 38.Find the value of x² + 2xy + y² when x = 6 and y = 2.
39. 39.Use a² − b² = (a + b)(a − b) to find 44² − 13².
40. 40.Use (a + b)(a − b) = a² − b² to find 52 × 48.

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