Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 218 · 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 63².
2. 2.Use (a + b)(a − b) = a² − b² to find 45 × 35.
3. 3.Find the value of x² − 2xy + y² when x = 4 and y = 3.
4. 4.Use (a + b)² = a² + 2ab + b² to find 28².
5. 5.Use a² − b² = (a + b)(a − b) to find 20² − 6².
6. 6.Find the value of x² − 2xy + y² when x = 10 and y = 3.
7. 7.Find the value of x² + 2xy + y² when x = 10 and y = 3.
8. 8.Use a² − b² = (a + b)(a − b) to find 61² − 55².
9. 9.Use a² − b² = (a + b)(a − b) to find 20² − 15².
10. 10.Use a² − b² = (a + b)(a − b) to find 81² − 72².
11. 11.Use (a − b)² = a² − 2ab + b² to find 44².
12. 12.Use (a + b)² = a² + 2ab + b² to find 106².
13. 13.Use (a + b)² = a² + 2ab + b² to find 87².
14. 14.Use a² − b² = (a + b)(a − b) to find 75² − 64².
15. 15.If a + b = 7 and ab = 6, what is a² + b²?
16. 16.If a + b = 15 and ab = 54, what is a² + b²?
17. 17.Use (a + b)² = a² + 2ab + b² to find 26².
18. 18.Use (a + b)² = a² + 2ab + b² to find 65².
19. 19.Use (a + b)(a − b) = a² − b² to find 33 × 27.
20. 20.Use (a − b)² = a² − 2ab + b² to find 45².
21. 21.Find the value of x² − 2xy + y² when x = 14 and y = 9.
22. 22.Use (a − b)² = a² − 2ab + b² to find 96².
23. 23.Use (a − b)² = a² − 2ab + b² to find 97².
24. 24.If a + b = 3 and ab = 2, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 84 × 76.
26. 26.Use a² − b² = (a + b)(a − b) to find 97² − 32².
27. 27.Use (a + b)² = a² + 2ab + b² to find 84².
28. 28.Use (a + b)(a − b) = a² − b² to find 101 × 99.
29. 29.Use (a − b)² = a² − 2ab + b² to find 23².
30. 30.Use (a + b)² = a² + 2ab + b² to find 22².
31. 31.Use (a − b)² = a² − 2ab + b² to find 72².
32. 32.If a + b = 13 and ab = 12, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 8 and y = 2.
34. 34.Use (a + b)(a − b) = a² − b² to find 36 × 24.
35. 35.Use (a − b)² = a² − 2ab + b² to find 73².
36. 36.Use a² − b² = (a + b)(a − b) to find 60² − 46².
37. 37.Use (a + b)² = a² + 2ab + b² to find 64².
38. 38.Use (a − b)² = a² − 2ab + b² to find 52².
39. 39.Use (a − b)² = a² − 2ab + b² to find 35².
40. 40.Use (a + b)(a − b) = a² − b² to find 32 × 28.

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