Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 869 · 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 53² − 39².
2. 2.Find the value of x² + 2xy + y² when x = 7 and y = 3.
3. 3.Use (a − b)² = a² − 2ab + b² to find 34².
4. 4.Use (a − b)² = a² − 2ab + b² to find 54².
5. 5.Find the value of x² + 2xy + y² when x = 6 and y = 4.
6. 6.Find the value of x² − y² when x = 3 and y = 2.
7. 7.Use (a + b)(a − b) = a² − b² to find 31 × 29.
8. 8.Use a² − b² = (a + b)(a − b) to find 69² − 51².
9. 9.Use (a + b)(a − b) = a² − b² to find 43 × 37.
10. 10.Use (a + b)² = a² + 2ab + b² to find 99².
11. 11.Use (a + b)(a − b) = a² − b² to find 82 × 78.
12. 12.Use (a + b)(a − b) = a² − b² to find 52 × 48.
13. 13.Use (a + b)² = a² + 2ab + b² to find 36².
14. 14.If a + b = 5 and ab = 6, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 64².
16. 16.Find the value of x² − 2xy + y² when x = 10 and y = 3.
17. 17.Use (a − b)² = a² − 2ab + b² to find 31².
18. 18.Use (a + b)² = a² + 2ab + b² to find 96².
19. 19.Use (a + b)² = a² + 2ab + b² to find 25².
20. 20.Use a² − b² = (a + b)(a − b) to find 59² − 47².
21. 21.Use (a − b)² = a² − 2ab + b² to find 52².
22. 22.Find the value of x² + 2xy + y² when x = 4 and y = 1.
23. 23.Find the value of x² + 2xy + y² when x = 9 and y = 5.
24. 24.Use (a − b)² = a² − 2ab + b² to find 97².
25. 25.If a − b = 5 and ab = 24, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 73².
27. 27.If a + b = 4 and ab = 3, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 44² − 1².
29. 29.Use (a + b)² = a² + 2ab + b² to find 75².
30. 30.Use (a + b)(a − b) = a² − b² to find 103 × 97.
31. 31.Find the value of x² − 2xy + y² when x = 13 and y = 4.
32. 32.Use (a + b)² = a² + 2ab + b² to find 22².
33. 33.Use (a + b)(a − b) = a² − b² to find 86 × 74.
34. 34.Find the value of x² + 2xy + y² when x = 14 and y = 5.
35. 35.Use (a − b)² = a² − 2ab + b² to find 28².
36. 36.Find the value of x² − y² when x = 10 and y = 2.
37. 37.Use a² − b² = (a + b)(a − b) to find 82² − 79².
38. 38.Use (a + b)(a − b) = a² − b² to find 39 × 21.
39. 39.Use (a − b)² = a² − 2ab + b² to find 55².
40. 40.Use (a − b)² = a² − 2ab + b² to find 35².

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