Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 117 · 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 15².
2. 2.Find the value of x² − 2xy + y² when x = 15 and y = 2.
3. 3.Find the value of x² − y² when x = 7 and y = 6.
4. 4.Use (a + b)(a − b) = a² − b² to find 45 × 35.
5. 5.Use (a − b)² = a² − 2ab + b² to find 25².
6. 6.Use (a + b)(a − b) = a² − b² to find 65 × 55.
7. 7.Use (a + b)² = a² + 2ab + b² to find 27².
8. 8.Use (a + b)² = a² + 2ab + b² to find 84².
9. 9.Use a² − b² = (a + b)(a − b) to find 27² − 2².
10. 10.Use a² − b² = (a + b)(a − b) to find 83² − 3².
11. 11.Use (a + b)(a − b) = a² − b² to find 43 × 37.
12. 12.Use (a + b)² = a² + 2ab + b² to find 51².
13. 13.Use (a + b)(a − b) = a² − b² to find 39 × 21.
14. 14.Use a² − b² = (a + b)(a − b) to find 27² − 1².
15. 15.Use (a + b)² = a² + 2ab + b² to find 102².
16. 16.Use (a + b)² = a² + 2ab + b² to find 105².
17. 17.Use (a − b)² = a² − 2ab + b² to find 19².
18. 18.If a − b = 4 and ab = 96, what is a² + b²?
19. 19.Find the value of x² + 2xy + y² when x = 5 and y = 2.
20. 20.Use a² − b² = (a + b)(a − b) to find 53² − 22².
21. 21.Use (a − b)² = a² − 2ab + b² to find 18².
22. 22.Use (a + b)² = a² + 2ab + b² to find 95².
23. 23.Use (a + b)² = a² + 2ab + b² to find 107².
24. 24.Use (a + b)(a − b) = a² − b² to find 106 × 94.
25. 25.Use (a − b)² = a² − 2ab + b² to find 72².
26. 26.Use a² − b² = (a + b)(a − b) to find 62² − 54².
27. 27.Use (a + b)(a − b) = a² − b² to find 34 × 26.
28. 28.Find the value of x² − 2xy + y² when x = 8 and y = 5.
29. 29.Find the value of x² − 2xy + y² when x = 5 and y = 1.
30. 30.Use (a + b)² = a² + 2ab + b² to find 29².
31. 31.Find the value of x² + 2xy + y² when x = 10 and y = 2.
32. 32.Find the value of x² − y² when x = 6 and y = 1.
33. 33.Use a² − b² = (a + b)(a − b) to find 74² − 72².
34. 34.Use a² − b² = (a + b)(a − b) to find 33² − 28².
35. 35.If a + b = 9 and ab = 20, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 17².
37. 37.Find the value of x² + 2xy + y² when x = 9 and y = 6.
38. 38.Use (a + b)² = a² + 2ab + b² to find 106².
39. 39.Use (a + b)² = a² + 2ab + b² to find 48².
40. 40.Use a² − b² = (a + b)(a − b) to find 46² − 45².

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