Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 151 · 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)(a − b) = a² − b² to find 106 × 94.
2. 2.Use (a + b)(a − b) = a² − b² to find 26 × 14.
3. 3.Use (a − b)² = a² − 2ab + b² to find 11².
4. 4.Use (a + b)(a − b) = a² − b² to find 66 × 54.
5. 5.Use (a + b)² = a² + 2ab + b² to find 62².
6. 6.If a + b = 9 and ab = 20, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 101 × 99.
8. 8.Find the value of x² − 2xy + y² when x = 13 and y = 5.
9. 9.Use (a + b)(a − b) = a² − b² to find 84 × 76.
10. 10.If a + b = 8 and ab = 7, what is a² + b²?
11. 11.Find the value of x² − y² when x = 3 and y = 1.
12. 12.Use (a − b)² = a² − 2ab + b² to find 69².
13. 13.Find the value of x² + 2xy + y² when x = 7 and y = 5.
14. 14.Use (a + b)² = a² + 2ab + b² to find 81².
15. 15.If a + b = 6 and ab = 8, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 59² − 6².
17. 17.Use (a − b)² = a² − 2ab + b² to find 35².
18. 18.Use a² − b² = (a + b)(a − b) to find 49² − 29².
19. 19.If a − b = 3 and ab = 108, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 75².
21. 21.Use (a − b)² = a² − 2ab + b² to find 12².
22. 22.If a − b = 3 and ab = 4, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 42².
24. 24.Use a² − b² = (a + b)(a − b) to find 29² − 10².
25. 25.Find the value of x² + 2xy + y² when x = 13 and y = 8.
26. 26.Use a² − b² = (a + b)(a − b) to find 60² − 38².
27. 27.If a + b = 15 and ab = 36, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 98².
29. 29.Find the value of x² − y² when x = 14 and y = 13.
30. 30.Use a² − b² = (a + b)(a − b) to find 99² − 76².
31. 31.Use (a − b)² = a² − 2ab + b² to find 83².
32. 32.If a + b = 3 and ab = 2, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 84².
34. 34.Use (a + b)(a − b) = a² − b² to find 92 × 88.
35. 35.Use (a − b)² = a² − 2ab + b² to find 96².
36. 36.Find the value of x² + 2xy + y² when x = 5 and y = 1.
37. 37.Use a² − b² = (a + b)(a − b) to find 51² − 40².
38. 38.Use (a − b)² = a² − 2ab + b² to find 63².
39. 39.Use (a + b)(a − b) = a² − b² to find 52 × 48.
40. 40.Use a² − b² = (a + b)(a − b) to find 74² − 58².

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