Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 892 · 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 72².
2. 2.Use (a + b)(a − b) = a² − b² to find 109 × 91.
3. 3.Use (a + b)² = a² + 2ab + b² to find 27².
4. 4.Find the value of x² − 2xy + y² when x = 5 and y = 2.
5. 5.Use (a + b)² = a² + 2ab + b² to find 37².
6. 6.Use (a − b)² = a² − 2ab + b² to find 95².
7. 7.Find the value of x² + 2xy + y² when x = 14 and y = 4.
8. 8.Use (a − b)² = a² − 2ab + b² to find 76².
9. 9.Use (a − b)² = a² − 2ab + b² to find 99².
10. 10.Use (a + b)² = a² + 2ab + b² to find 38².
11. 11.Use (a − b)² = a² − 2ab + b² to find 19².
12. 12.If a − b = 1 and ab = 132, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 49² − 43².
14. 14.Use (a + b)(a − b) = a² − b² to find 83 × 77.
15. 15.Use a² − b² = (a + b)(a − b) to find 21² − 12².
16. 16.Use a² − b² = (a + b)(a − b) to find 29² − 25².
17. 17.Use (a + b)(a − b) = a² − b² to find 29 × 11.
18. 18.Use a² − b² = (a + b)(a − b) to find 26² − 12².
19. 19.Find the value of x² − y² when x = 15 and y = 12.
20. 20.Use a² − b² = (a + b)(a − b) to find 77² − 58².
21. 21.Use (a − b)² = a² − 2ab + b² to find 91².
22. 22.Use (a + b)² = a² + 2ab + b² to find 25².
23. 23.Use (a + b)² = a² + 2ab + b² to find 16².
24. 24.Find the value of x² + 2xy + y² when x = 15 and y = 13.
25. 25.Use (a + b)(a − b) = a² − b² to find 85 × 75.
26. 26.Use (a + b)(a − b) = a² − b² to find 37 × 23.
27. 27.Use (a − b)² = a² − 2ab + b² to find 56².
28. 28.Find the value of x² + 2xy + y² when x = 6 and y = 1.
29. 29.Use a² − b² = (a + b)(a − b) to find 43² − 27².
30. 30.If a + b = 15 and ab = 56, what is a² + b²?
31. 31.Find the value of x² + 2xy + y² when x = 7 and y = 2.
32. 32.Use (a − b)² = a² − 2ab + b² to find 92².
33. 33.Use (a + b)² = a² + 2ab + b² to find 83².
34. 34.Use a² − b² = (a + b)(a − b) to find 41² − 16².
35. 35.Use (a + b)(a − b) = a² − b² to find 89 × 71.
36. 36.If a − b = 3 and ab = 4, what is a² + b²?
37. 37.Find the value of x² + 2xy + y² when x = 3 and y = 1.
38. 38.Use (a + b)² = a² + 2ab + b² to find 106².
39. 39.Use (a + b)(a − b) = a² − b² to find 28 × 12.
40. 40.Use (a − b)² = a² − 2ab + b² to find 12².

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