Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 421 · 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 39² − 35².
2. 2.Use (a + b)² = a² + 2ab + b² to find 75².
3. 3.Find the value of x² − 2xy + y² when x = 14 and y = 2.
4. 4.Use a² − b² = (a + b)(a − b) to find 26² − 18².
5. 5.Use (a + b)² = a² + 2ab + b² to find 33².
6. 6.Use (a − b)² = a² − 2ab + b² to find 12².
7. 7.Use (a + b)(a − b) = a² − b² to find 105 × 95.
8. 8.Use a² − b² = (a + b)(a − b) to find 63² − 11².
9. 9.Use (a + b)(a − b) = a² − b² to find 37 × 23.
10. 10.Use (a + b)² = a² + 2ab + b² to find 48².
11. 11.Use (a + b)(a − b) = a² − b² to find 92 × 88.
12. 12.Use (a + b)² = a² + 2ab + b² to find 85².
13. 13.If a + b = 6 and ab = 8, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 17².
15. 15.Use (a + b)(a − b) = a² − b² to find 76 × 64.
16. 16.If a + b = 5 and ab = 4, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 32² − 25².
18. 18.Find the value of x² + 2xy + y² when x = 4 and y = 3.
19. 19.Find the value of x² + 2xy + y² when x = 9 and y = 2.
20. 20.Use (a + b)² = a² + 2ab + b² to find 97².
21. 21.If a − b = 6 and ab = 16, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 86².
23. 23.Use (a + b)² = a² + 2ab + b² to find 32².
24. 24.Use a² − b² = (a + b)(a − b) to find 36² − 5².
25. 25.If a − b = 2 and ab = 3, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 81².
27. 27.Use a² − b² = (a + b)(a − b) to find 36² − 18².
28. 28.Use (a + b)(a − b) = a² − b² to find 72 × 68.
29. 29.Use (a + b)(a − b) = a² − b² to find 41 × 39.
30. 30.Find the value of x² − 2xy + y² when x = 3 and y = 2.
31. 31.Find the value of x² − 2xy + y² when x = 13 and y = 2.
32. 32.Use (a + b)² = a² + 2ab + b² to find 105².
33. 33.Use (a + b)² = a² + 2ab + b² to find 84².
34. 34.Use (a + b)² = a² + 2ab + b² to find 18².
35. 35.Use a² − b² = (a + b)(a − b) to find 74² − 19².
36. 36.Use a² − b² = (a + b)(a − b) to find 53² − 3².
37. 37.Use (a − b)² = a² − 2ab + b² to find 67².
38. 38.Use (a + b)² = a² + 2ab + b² to find 71².
39. 39.Use (a + b)² = a² + 2ab + b² to find 93².
40. 40.Use (a − b)² = a² − 2ab + b² to find 31².

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