Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 335 · 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 81 × 79.
2. 2.If a + b = 17 and ab = 70, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 56 × 44.
4. 4.Use (a + b)² = a² + 2ab + b² to find 79².
5. 5.Use (a + b)² = a² + 2ab + b² to find 66².
6. 6.If a − b = 1 and ab = 2, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 22².
8. 8.Use (a + b)² = a² + 2ab + b² to find 57².
9. 9.Use (a − b)² = a² − 2ab + b² to find 54².
10. 10.Find the value of x² + 2xy + y² when x = 9 and y = 7.
11. 11.Use (a + b)(a − b) = a² − b² to find 42 × 38.
12. 12.Use (a + b)² = a² + 2ab + b² to find 18².
13. 13.If a − b = 5 and ab = 24, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 42².
15. 15.Find the value of x² − y² when x = 14 and y = 2.
16. 16.Use a² − b² = (a + b)(a − b) to find 57² − 27².
17. 17.Find the value of x² − 2xy + y² when x = 13 and y = 8.
18. 18.If a + b = 16 and ab = 55, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 27².
20. 20.Use (a + b)² = a² + 2ab + b² to find 22².
21. 21.Find the value of x² + 2xy + y² when x = 4 and y = 3.
22. 22.Use (a + b)² = a² + 2ab + b² to find 73².
23. 23.Use (a + b)(a − b) = a² − b² to find 68 × 52.
24. 24.Use (a − b)² = a² − 2ab + b² to find 95².
25. 25.Use (a + b)(a − b) = a² − b² to find 91 × 89.
26. 26.Use (a − b)² = a² − 2ab + b² to find 55².
27. 27.Use a² − b² = (a + b)(a − b) to find 36² − 31².
28. 28.Use a² − b² = (a + b)(a − b) to find 49² − 23².
29. 29.Use (a − b)² = a² − 2ab + b² to find 68².
30. 30.Find the value of x² − y² when x = 11 and y = 4.
31. 31.Use a² − b² = (a + b)(a − b) to find 68² − 56².
32. 32.Use a² − b² = (a + b)(a − b) to find 30² − 12².
33. 33.Use (a − b)² = a² − 2ab + b² to find 74².
34. 34.Use a² − b² = (a + b)(a − b) to find 54² − 10².
35. 35.Use (a + b)² = a² + 2ab + b² to find 108².
36. 36.Use a² − b² = (a + b)(a − b) to find 95² − 60².
37. 37.Use (a + b)² = a² + 2ab + b² to find 21².
38. 38.Use a² − b² = (a + b)(a − b) to find 54² − 5².
39. 39.Find the value of x² + 2xy + y² when x = 13 and y = 4.
40. 40.Use (a + b)² = a² + 2ab + b² to find 56².

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