Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 362 · 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 83².
2. 2.Find the value of x² + 2xy + y² when x = 6 and y = 3.
3. 3.Use (a − b)² = a² − 2ab + b² to find 87².
4. 4.If a − b = 4 and ab = 5, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 26 × 14.
6. 6.If a − b = 1 and ab = 42, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 83² − 73².
8. 8.Use a² − b² = (a + b)(a − b) to find 88² − 69².
9. 9.Use a² − b² = (a + b)(a − b) to find 96² − 75².
10. 10.Use (a − b)² = a² − 2ab + b² to find 17².
11. 11.Use (a − b)² = a² − 2ab + b² to find 36².
12. 12.Use a² − b² = (a + b)(a − b) to find 99² − 3².
13. 13.Use (a + b)(a − b) = a² − b² to find 23 × 17.
14. 14.Use a² − b² = (a + b)(a − b) to find 91² − 17².
15. 15.Use (a + b)(a − b) = a² − b² to find 49 × 31.
16. 16.Use (a + b)² = a² + 2ab + b² to find 106².
17. 17.Find the value of x² − 2xy + y² when x = 11 and y = 7.
18. 18.Use a² − b² = (a + b)(a − b) to find 50² − 3².
19. 19.Use (a + b)² = a² + 2ab + b² to find 56².
20. 20.Use (a + b)(a − b) = a² − b² to find 55 × 45.
21. 21.Use (a + b)(a − b) = a² − b² to find 24 × 16.
22. 22.Use (a + b)² = a² + 2ab + b² to find 94².
23. 23.Use (a + b)(a − b) = a² − b² to find 58 × 42.
24. 24.If a − b = 9 and ab = 10, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 73 × 67.
26. 26.If a + b = 6 and ab = 8, what is a² + b²?
27. 27.Find the value of x² + 2xy + y² when x = 11 and y = 1.
28. 28.Use (a + b)² = a² + 2ab + b² to find 41².
29. 29.Use (a − b)² = a² − 2ab + b² to find 96².
30. 30.Use a² − b² = (a + b)(a − b) to find 93² − 43².
31. 31.Use a² − b² = (a + b)(a − b) to find 89² − 83².
32. 32.Find the value of x² + 2xy + y² when x = 10 and y = 5.
33. 33.Use a² − b² = (a + b)(a − b) to find 61² − 31².
34. 34.Use (a − b)² = a² − 2ab + b² to find 11².
35. 35.Find the value of x² − y² when x = 13 and y = 7.
36. 36.Use a² − b² = (a + b)(a − b) to find 35² − 5².
37. 37.Use (a − b)² = a² − 2ab + b² to find 75².
38. 38.Use (a + b)² = a² + 2ab + b² to find 83².
39. 39.Use (a + b)(a − b) = a² − b² to find 47 × 33.
40. 40.Use (a + b)² = a² + 2ab + b² to find 35².

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