Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 650 · 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 94 × 86.
2. 2.Use (a + b)² = a² + 2ab + b² to find 102².
3. 3.Use (a + b)² = a² + 2ab + b² to find 18².
4. 4.Find the value of x² − 2xy + y² when x = 15 and y = 10.
5. 5.Use (a + b)(a − b) = a² − b² to find 42 × 38.
6. 6.If a − b = 4 and ab = 5, what is a² + b²?
7. 7.Find the value of x² + 2xy + y² when x = 15 and y = 13.
8. 8.Use (a − b)² = a² − 2ab + b² to find 52².
9. 9.Find the value of x² − y² when x = 12 and y = 7.
10. 10.Use a² − b² = (a + b)(a − b) to find 36² − 19².
11. 11.Use (a − b)² = a² − 2ab + b² to find 17².
12. 12.Use a² − b² = (a + b)(a − b) to find 93² − 68².
13. 13.Use a² − b² = (a + b)(a − b) to find 35² − 31².
14. 14.Use a² − b² = (a + b)(a − b) to find 43² − 1².
15. 15.Use (a + b)(a − b) = a² − b² to find 88 × 72.
16. 16.Use (a − b)² = a² − 2ab + b² to find 19².
17. 17.Use (a + b)(a − b) = a² − b² to find 64 × 56.
18. 18.Use (a − b)² = a² − 2ab + b² to find 94².
19. 19.Use (a − b)² = a² − 2ab + b² to find 21².
20. 20.Use a² − b² = (a + b)(a − b) to find 95² − 79².
21. 21.Use (a − b)² = a² − 2ab + b² to find 13².
22. 22.Use (a + b)² = a² + 2ab + b² to find 77².
23. 23.Use (a + b)² = a² + 2ab + b² to find 72².
24. 24.Use (a + b)² = a² + 2ab + b² to find 82².
25. 25.Use a² − b² = (a + b)(a − b) to find 72² − 51².
26. 26.If a − b = 7 and ab = 8, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 108².
28. 28.Use (a + b)(a − b) = a² − b² to find 29 × 11.
29. 29.Use a² − b² = (a + b)(a − b) to find 26² − 12².
30. 30.Use (a + b)² = a² + 2ab + b² to find 13².
31. 31.Use (a + b)² = a² + 2ab + b² to find 28².
32. 32.If a + b = 14 and ab = 33, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 29².
34. 34.If a + b = 5 and ab = 6, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 27² − 10².
36. 36.Use a² − b² = (a + b)(a − b) to find 54² − 49².
37. 37.Use a² − b² = (a + b)(a − b) to find 20² − 3².
38. 38.Use (a + b)² = a² + 2ab + b² to find 38².
39. 39.Use a² − b² = (a + b)(a − b) to find 31² − 4².
40. 40.Use (a + b)² = a² + 2ab + b² to find 16².

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