Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 242 · 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 88².
2. 2.Use a² − b² = (a + b)(a − b) to find 75² − 58².
3. 3.If a + b = 11 and ab = 18, what is a² + b²?
4. 4.Find the value of x² − y² when x = 7 and y = 4.
5. 5.Use (a + b)(a − b) = a² − b² to find 92 × 88.
6. 6.If a − b = 2 and ab = 8, what is a² + b²?
7. 7.If a + b = 15 and ab = 56, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 38² − 10².
9. 9.Use a² − b² = (a + b)(a − b) to find 95² − 65².
10. 10.Use (a + b)(a − b) = a² − b² to find 71 × 69.
11. 11.Use (a + b)(a − b) = a² − b² to find 44 × 36.
12. 12.Use (a + b)(a − b) = a² − b² to find 68 × 52.
13. 13.Use (a − b)² = a² − 2ab + b² to find 41².
14. 14.Use (a + b)² = a² + 2ab + b² to find 54².
15. 15.Find the value of x² − y² when x = 4 and y = 3.
16. 16.Find the value of x² − y² when x = 5 and y = 4.
17. 17.Use (a − b)² = a² − 2ab + b² to find 54².
18. 18.Use (a + b)² = a² + 2ab + b² to find 56².
19. 19.Use (a − b)² = a² − 2ab + b² to find 38².
20. 20.Use (a + b)² = a² + 2ab + b² to find 101².
21. 21.If a − b = 1 and ab = 2, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 11².
23. 23.Find the value of x² − 2xy + y² when x = 11 and y = 9.
24. 24.Use a² − b² = (a + b)(a − b) to find 92² − 17².
25. 25.Find the value of x² − 2xy + y² when x = 14 and y = 3.
26. 26.Use (a − b)² = a² − 2ab + b² to find 81².
27. 27.Use (a + b)² = a² + 2ab + b² to find 103².
28. 28.Use (a + b)² = a² + 2ab + b² to find 49².
29. 29.Use (a + b)² = a² + 2ab + b² to find 81².
30. 30.Find the value of x² − 2xy + y² when x = 3 and y = 2.
31. 31.Use a² − b² = (a + b)(a − b) to find 98² − 68².
32. 32.Use (a + b)(a − b) = a² − b² to find 58 × 42.
33. 33.Find the value of x² − 2xy + y² when x = 14 and y = 11.
34. 34.Use (a + b)(a − b) = a² − b² to find 28 × 12.
35. 35.Use (a + b)² = a² + 2ab + b² to find 26².
36. 36.If a − b = 2 and ab = 15, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 36².
38. 38.If a − b = 3 and ab = 18, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 77² − 66².
40. 40.Use a² − b² = (a + b)(a − b) to find 95² − 25².

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