Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 286 · 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 60² − 8².
2. 2.Use (a + b)(a − b) = a² − b² to find 63 × 57.
3. 3.If a − b = 2 and ab = 3, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 31².
5. 5.Use (a − b)² = a² − 2ab + b² to find 28².
6. 6.Find the value of x² − y² when x = 11 and y = 10.
7. 7.Use a² − b² = (a + b)(a − b) to find 66² − 13².
8. 8.Use (a + b)² = a² + 2ab + b² to find 89².
9. 9.Use (a + b)² = a² + 2ab + b² to find 34².
10. 10.Use (a − b)² = a² − 2ab + b² to find 17².
11. 11.Find the value of x² + 2xy + y² when x = 11 and y = 9.
12. 12.Use (a − b)² = a² − 2ab + b² to find 34².
13. 13.If a − b = 1 and ab = 42, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 67 × 53.
15. 15.Use (a + b)(a − b) = a² − b² to find 84 × 76.
16. 16.Use (a + b)(a − b) = a² − b² to find 107 × 93.
17. 17.Find the value of x² − y² when x = 3 and y = 1.
18. 18.Use (a + b)² = a² + 2ab + b² to find 91².
19. 19.Use (a − b)² = a² − 2ab + b² to find 21².
20. 20.If a + b = 3 and ab = 2, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 45².
22. 22.If a − b = 6 and ab = 40, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 15².
24. 24.Use a² − b² = (a + b)(a − b) to find 71² − 23².
25. 25.Use (a − b)² = a² − 2ab + b² to find 57².
26. 26.Use a² − b² = (a + b)(a − b) to find 88² − 3².
27. 27.Use (a + b)(a − b) = a² − b² to find 71 × 69.
28. 28.If a − b = 3 and ab = 10, what is a² + b²?
29. 29.If a + b = 9 and ab = 18, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 99².
31. 31.Find the value of x² − y² when x = 10 and y = 2.
32. 32.Use a² − b² = (a + b)(a − b) to find 72² − 71².
33. 33.Find the value of x² − y² when x = 5 and y = 1.
34. 34.If a + b = 8 and ab = 7, what is a² + b²?
35. 35.Find the value of x² − 2xy + y² when x = 5 and y = 2.
36. 36.If a + b = 9 and ab = 20, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 68² − 18².
38. 38.If a − b = 2 and ab = 8, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 102 × 98.
40. 40.If a + b = 12 and ab = 27, what is a² + b²?

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