Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 735 · 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 a² − b² = (a + b)(a − b) to find 32² − 10².
2. 2.Use a² − b² = (a + b)(a − b) to find 55² − 49².
3. 3.Use (a − b)² = a² − 2ab + b² to find 66².
4. 4.If a − b = 1 and ab = 12, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 77 × 63.
6. 6.Use (a − b)² = a² − 2ab + b² to find 56².
7. 7.Use (a + b)(a − b) = a² − b² to find 65 × 55.
8. 8.Use (a + b)² = a² + 2ab + b² to find 103².
9. 9.If a − b = 2 and ab = 48, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 37².
11. 11.Use a² − b² = (a + b)(a − b) to find 20² − 5².
12. 12.If a − b = 1 and ab = 56, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 72 × 68.
14. 14.Find the value of x² + 2xy + y² when x = 12 and y = 10.
15. 15.Use a² − b² = (a + b)(a − b) to find 26² − 20².
16. 16.If a + b = 4 and ab = 3, what is a² + b²?
17. 17.If a − b = 1 and ab = 72, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 94² − 53².
19. 19.Use a² − b² = (a + b)(a − b) to find 59² − 2².
20. 20.If a + b = 15 and ab = 54, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 88².
22. 22.Use (a − b)² = a² − 2ab + b² to find 68².
23. 23.Use (a + b)(a − b) = a² − b² to find 49 × 31.
24. 24.Use (a − b)² = a² − 2ab + b² to find 69².
25. 25.If a + b = 9 and ab = 20, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 79 × 61.
27. 27.Find the value of x² + 2xy + y² when x = 4 and y = 3.
28. 28.Find the value of x² + 2xy + y² when x = 4 and y = 2.
29. 29.Use (a + b)² = a² + 2ab + b² to find 96².
30. 30.Use (a − b)² = a² − 2ab + b² to find 46².
31. 31.Use (a − b)² = a² − 2ab + b² to find 25².
32. 32.Use (a + b)² = a² + 2ab + b² to find 59².
33. 33.Use a² − b² = (a + b)(a − b) to find 72² − 46².
34. 34.Use a² − b² = (a + b)(a − b) to find 41² − 10².
35. 35.Use (a + b)(a − b) = a² − b² to find 52 × 48.
36. 36.Use (a + b)(a − b) = a² − b² to find 99 × 81.
37. 37.Use (a + b)(a − b) = a² − b² to find 33 × 27.
38. 38.Use (a − b)² = a² − 2ab + b² to find 76².
39. 39.Find the value of x² − y² when x = 3 and y = 1.
40. 40.Use a² − b² = (a + b)(a − b) to find 33² − 16².

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