Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 700 · 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 71².
2. 2.Use (a − b)² = a² − 2ab + b² to find 94².
3. 3.Use a² − b² = (a + b)(a − b) to find 89² − 19².
4. 4.Find the value of x² + 2xy + y² when x = 8 and y = 1.
5. 5.Use (a + b)(a − b) = a² − b² to find 42 × 38.
6. 6.Use (a + b)² = a² + 2ab + b² to find 35².
7. 7.If a + b = 20 and ab = 99, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 84² − 3².
9. 9.Find the value of x² − y² when x = 7 and y = 4.
10. 10.Use (a − b)² = a² − 2ab + b² to find 32².
11. 11.If a − b = 3 and ab = 88, what is a² + b²?
12. 12.If a + b = 11 and ab = 18, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 39².
14. 14.Use (a + b)² = a² + 2ab + b² to find 81².
15. 15.Use (a + b)² = a² + 2ab + b² to find 41².
16. 16.Find the value of x² − y² when x = 12 and y = 1.
17. 17.If a + b = 3 and ab = 2, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 76 × 64.
19. 19.If a − b = 3 and ab = 28, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 63².
21. 21.Use (a − b)² = a² − 2ab + b² to find 47².
22. 22.If a − b = 8 and ab = 33, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 66 × 54.
24. 24.Use a² − b² = (a + b)(a − b) to find 25² − 18².
25. 25.Use a² − b² = (a + b)(a − b) to find 38² − 5².
26. 26.Use (a − b)² = a² − 2ab + b² to find 92².
27. 27.Use a² − b² = (a + b)(a − b) to find 96² − 57².
28. 28.Use (a − b)² = a² − 2ab + b² to find 95².
29. 29.If a − b = 2 and ab = 8, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 44².
31. 31.Use (a + b)(a − b) = a² − b² to find 98 × 82.
32. 32.Use a² − b² = (a + b)(a − b) to find 83² − 17².
33. 33.Find the value of x² − y² when x = 9 and y = 2.
34. 34.If a − b = 3 and ab = 18, what is a² + b²?
35. 35.If a + b = 6 and ab = 5, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 95².
37. 37.Use (a + b)(a − b) = a² − b² to find 52 × 48.
38. 38.Use a² − b² = (a + b)(a − b) to find 23² − 10².
39. 39.Find the value of x² − y² when x = 3 and y = 2.
40. 40.Find the value of x² + 2xy + y² when x = 11 and y = 6.

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