Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 168 · 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.If a − b = 1 and ab = 2, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 62² − 20².
3. 3.Use (a + b)(a − b) = a² − b² to find 81 × 79.
4. 4.Find the value of x² + 2xy + y² when x = 6 and y = 5.
5. 5.Use (a − b)² = a² − 2ab + b² to find 96².
6. 6.Use (a − b)² = a² − 2ab + b² to find 43².
7. 7.Use (a − b)² = a² − 2ab + b² to find 13².
8. 8.Find the value of x² − y² when x = 4 and y = 2.
9. 9.Use (a + b)(a − b) = a² − b² to find 21 × 19.
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.Find the value of x² − 2xy + y² when x = 6 and y = 2.
12. 12.Use (a + b)(a − b) = a² − b² to find 45 × 35.
13. 13.Use (a + b)² = a² + 2ab + b² to find 11².
14. 14.Use a² − b² = (a + b)(a − b) to find 89² − 76².
15. 15.Use a² − b² = (a + b)(a − b) to find 45² − 32².
16. 16.Use (a − b)² = a² − 2ab + b² to find 93².
17. 17.Use (a − b)² = a² − 2ab + b² to find 91².
18. 18.Use (a − b)² = a² − 2ab + b² to find 15².
19. 19.Use (a + b)² = a² + 2ab + b² to find 82².
20. 20.Use (a + b)(a − b) = a² − b² to find 105 × 95.
21. 21.Use (a + b)² = a² + 2ab + b² to find 108².
22. 22.Use (a + b)² = a² + 2ab + b² to find 102².
23. 23.Use (a − b)² = a² − 2ab + b² to find 18².
24. 24.Use (a − b)² = a² − 2ab + b² to find 72².
25. 25.Use (a + b)² = a² + 2ab + b² to find 32².
26. 26.Use (a + b)(a − b) = a² − b² to find 91 × 89.
27. 27.Use (a + b)(a − b) = a² − b² to find 36 × 24.
28. 28.Use a² − b² = (a + b)(a − b) to find 41² − 14².
29. 29.Use a² − b² = (a + b)(a − b) to find 64² − 25².
30. 30.Use (a + b)² = a² + 2ab + b² to find 78².
31. 31.Use a² − b² = (a + b)(a − b) to find 90² − 18².
32. 32.Use (a + b)(a − b) = a² − b² to find 99 × 81.
33. 33.Find the value of x² − 2xy + y² when x = 15 and y = 2.
34. 34.Use a² − b² = (a + b)(a − b) to find 79² − 36².
35. 35.Use a² − b² = (a + b)(a − b) to find 42² − 13².
36. 36.Use (a − b)² = a² − 2ab + b² to find 83².
37. 37.Use (a − b)² = a² − 2ab + b² to find 84².
38. 38.Use (a + b)² = a² + 2ab + b² to find 54².
39. 39.Use (a − b)² = a² − 2ab + b² to find 71².
40. 40.Use (a + b)(a − b) = a² − b² to find 61 × 59.

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