Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 693 · 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 47² − 5².
2. 2.If a − b = 9 and ab = 10, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 21 × 19.
4. 4.Find the value of x² − y² when x = 13 and y = 10.
5. 5.Find the value of x² − y² when x = 5 and y = 3.
6. 6.If a + b = 6 and ab = 5, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 76².
8. 8.Find the value of x² − 2xy + y² when x = 11 and y = 1.
9. 9.Use (a + b)² = a² + 2ab + b² to find 83².
10. 10.Find the value of x² − 2xy + y² when x = 10 and y = 2.
11. 11.Use (a − b)² = a² − 2ab + b² to find 62².
12. 12.Use (a + b)² = a² + 2ab + b² to find 71².
13. 13.Use a² − b² = (a + b)(a − b) to find 97² − 18².
14. 14.Use (a + b)(a − b) = a² − b² to find 65 × 55.
15. 15.If a − b = 1 and ab = 2, what is a² + b²?
16. 16.Find the value of x² − y² when x = 7 and y = 2.
17. 17.Find the value of x² − 2xy + y² when x = 9 and y = 5.
18. 18.Use a² − b² = (a + b)(a − b) to find 30² − 6².
19. 19.Use a² − b² = (a + b)(a − b) to find 69² − 27².
20. 20.If a + b = 19 and ab = 90, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 39².
22. 22.Use a² − b² = (a + b)(a − b) to find 38² − 20².
23. 23.Use (a + b)(a − b) = a² − b² to find 46 × 34.
24. 24.If a − b = 1 and ab = 56, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 7 and y = 1.
26. 26.Use (a + b)² = a² + 2ab + b² to find 63².
27. 27.Use (a + b)(a − b) = a² − b² to find 57 × 43.
28. 28.Use a² − b² = (a + b)(a − b) to find 72² − 38².
29. 29.Use a² − b² = (a + b)(a − b) to find 60² − 58².
30. 30.If a + b = 9 and ab = 14, what is a² + b²?
31. 31.Find the value of x² − y² when x = 15 and y = 3.
32. 32.Use (a − b)² = a² − 2ab + b² to find 57².
33. 33.Use (a − b)² = a² − 2ab + b² to find 69².
34. 34.Use (a + b)(a − b) = a² − b² to find 101 × 99.
35. 35.If a + b = 15 and ab = 50, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 64 × 56.
37. 37.Use (a + b)² = a² + 2ab + b² to find 54².
38. 38.If a + b = 10 and ab = 24, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 74².
40. 40.Find the value of x² − 2xy + y² when x = 14 and y = 4.

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