Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 371 · 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 − y² when x = 7 and y = 2.
2. 2.If a + b = 13 and ab = 40, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 78².
4. 4.Use (a + b)² = a² + 2ab + b² to find 77².
5. 5.Use (a + b)(a − b) = a² − b² to find 24 × 16.
6. 6.If a + b = 5 and ab = 4, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 51².
8. 8.Use (a + b)² = a² + 2ab + b² to find 73².
9. 9.Use (a + b)(a − b) = a² − b² to find 38 × 22.
10. 10.If a − b = 3 and ab = 10, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 84 × 76.
12. 12.Use a² − b² = (a + b)(a − b) to find 45² − 1².
13. 13.Use (a + b)(a − b) = a² − b² to find 41 × 39.
14. 14.Use a² − b² = (a + b)(a − b) to find 91² − 29².
15. 15.Find the value of x² + 2xy + y² when x = 6 and y = 2.
16. 16.Use a² − b² = (a + b)(a − b) to find 21² − 15².
17. 17.Use a² − b² = (a + b)(a − b) to find 97² − 24².
18. 18.Use (a − b)² = a² − 2ab + b² to find 77².
19. 19.Use (a + b)(a − b) = a² − b² to find 109 × 91.
20. 20.If a + b = 10 and ab = 9, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 85² − 5².
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 3.
23. 23.Use (a + b)² = a² + 2ab + b² to find 34².
24. 24.If a − b = 2 and ab = 24, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 57².
26. 26.Use (a + b)² = a² + 2ab + b² to find 59².
27. 27.Use (a − b)² = a² − 2ab + b² to find 13².
28. 28.Use (a + b)² = a² + 2ab + b² to find 81².
29. 29.Use (a + b)² = a² + 2ab + b² to find 37².
30. 30.If a + b = 7 and ab = 10, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 71².
32. 32.If a + b = 7 and ab = 6, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 3 and y = 1.
34. 34.Use (a + b)² = a² + 2ab + b² to find 31².
35. 35.Find the value of x² − 2xy + y² when x = 5 and y = 4.
36. 36.If a − b = 5 and ab = 6, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 56².
38. 38.Find the value of x² − 2xy + y² when x = 13 and y = 1.
39. 39.If a + b = 3 and ab = 2, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 89² − 75².

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