Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 387 · 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)² = a² − 2ab + b² to find 68².
2. 2.Use (a − b)² = a² − 2ab + b² to find 82².
3. 3.If a − b = 1 and ab = 6, what is a² + b²?
4. 4.If a + b = 6 and ab = 8, what is a² + b²?
5. 5.Use a² − b² = (a + b)(a − b) to find 79² − 46².
6. 6.If a − b = 1 and ab = 2, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 45².
8. 8.Use a² − b² = (a + b)(a − b) to find 81² − 17².
9. 9.Use (a + b)(a − b) = a² − b² to find 84 × 76.
10. 10.Use (a + b)(a − b) = a² − b² to find 104 × 96.
11. 11.Find the value of x² + 2xy + y² when x = 14 and y = 5.
12. 12.Use (a − b)² = a² − 2ab + b² to find 17².
13. 13.Find the value of x² − y² when x = 11 and y = 10.
14. 14.Use (a + b)² = a² + 2ab + b² to find 94².
15. 15.Use (a − b)² = a² − 2ab + b² to find 94².
16. 16.If a + b = 16 and ab = 48, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 58².
18. 18.If a + b = 9 and ab = 20, what is a² + b²?
19. 19.Find the value of x² + 2xy + y² when x = 11 and y = 9.
20. 20.Find the value of x² + 2xy + y² when x = 5 and y = 4.
21. 21.If a + b = 12 and ab = 32, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 14².
23. 23.Use (a − b)² = a² − 2ab + b² to find 49².
24. 24.Use (a + b)² = a² + 2ab + b² to find 102².
25. 25.Find the value of x² + 2xy + y² when x = 9 and y = 2.
26. 26.Find the value of x² − y² when x = 6 and y = 5.
27. 27.Use a² − b² = (a + b)(a − b) to find 23² − 10².
28. 28.Use (a + b)(a − b) = a² − b² to find 58 × 42.
29. 29.Use (a − b)² = a² − 2ab + b² to find 48².
30. 30.Use a² − b² = (a + b)(a − b) to find 34² − 23².
31. 31.Use a² − b² = (a + b)(a − b) to find 94² − 56².
32. 32.Use a² − b² = (a + b)(a − b) to find 21² − 16².
33. 33.Use (a + b)(a − b) = a² − b² to find 36 × 24.
34. 34.Use a² − b² = (a + b)(a − b) to find 97² − 71².
35. 35.Find the value of x² + 2xy + y² when x = 11 and y = 1.
36. 36.Use (a − b)² = a² − 2ab + b² to find 46².
37. 37.Use (a − b)² = a² − 2ab + b² to find 26².
38. 38.Use (a + b)(a − b) = a² − b² to find 72 × 68.
39. 39.Find the value of x² + 2xy + y² when x = 11 and y = 7.
40. 40.Find the value of x² + 2xy + y² when x = 10 and y = 7.

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