Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 495 · 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.Find the value of x² − 2xy + y² when x = 3 and y = 2.
2. 2.Use (a + b)(a − b) = a² − b² to find 24 × 16.
3. 3.Use a² − b² = (a + b)(a − b) to find 22² − 9².
4. 4.Use (a − b)² = a² − 2ab + b² to find 19².
5. 5.If a + b = 6 and ab = 8, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 37 × 23.
7. 7.If a + b = 8 and ab = 7, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 30² − 7².
9. 9.Use (a − b)² = a² − 2ab + b² to find 58².
10. 10.Use (a − b)² = a² − 2ab + b² to find 25².
11. 11.Use a² − b² = (a + b)(a − b) to find 87² − 86².
12. 12.Find the value of x² − 2xy + y² when x = 11 and y = 9.
13. 13.Find the value of x² − y² when x = 15 and y = 9.
14. 14.If a + b = 5 and ab = 6, what is a² + b²?
15. 15.If a + b = 3 and ab = 2, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 21² − 13².
17. 17.If a − b = 1 and ab = 20, what is a² + b²?
18. 18.If a + b = 23 and ab = 132, what is a² + b²?
19. 19.Use (a + b)(a − b) = a² − b² to find 33 × 27.
20. 20.Find the value of x² + 2xy + y² when x = 11 and y = 1.
21. 21.Use (a − b)² = a² − 2ab + b² to find 93².
22. 22.If a − b = 3 and ab = 4, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 88 × 72.
24. 24.Use a² − b² = (a + b)(a − b) to find 58² − 22².
25. 25.Use (a − b)² = a² − 2ab + b² to find 54².
26. 26.Use (a − b)² = a² − 2ab + b² to find 77².
27. 27.Use (a + b)(a − b) = a² − b² to find 66 × 54.
28. 28.Use (a + b)(a − b) = a² − b² to find 97 × 83.
29. 29.Use (a + b)² = a² + 2ab + b² to find 109².
30. 30.Use (a − b)² = a² − 2ab + b² to find 13².
31. 31.Use (a + b)² = a² + 2ab + b² to find 56².
32. 32.Use (a + b)(a − b) = a² − b² to find 31 × 29.
33. 33.Use a² − b² = (a + b)(a − b) to find 79² − 71².
34. 34.Use (a + b)² = a² + 2ab + b² to find 95².
35. 35.Use a² − b² = (a + b)(a − b) to find 71² − 59².
36. 36.Use (a + b)(a − b) = a² − b² to find 109 × 91.
37. 37.Use (a + b)(a − b) = a² − b² to find 79 × 61.
38. 38.Use (a + b)² = a² + 2ab + b² to find 29².
39. 39.If a − b = 1 and ab = 132, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 82².

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