Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 452 · 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.Find the value of x² − 2xy + y² when x = 8 and y = 7.
2. 2.Use (a + b)(a − b) = a² − b² to find 38 × 22.
3. 3.Use (a + b)² = a² + 2ab + b² to find 23².
4. 4.Find the value of x² − y² when x = 8 and y = 1.
5. 5.If a + b = 14 and ab = 48, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 97².
7. 7.Find the value of x² − y² when x = 13 and y = 2.
8. 8.Use (a + b)² = a² + 2ab + b² to find 87².
9. 9.Use (a + b)² = a² + 2ab + b² to find 29².
10. 10.Use (a + b)² = a² + 2ab + b² to find 64².
11. 11.Use (a + b)(a − b) = a² − b² to find 81 × 79.
12. 12.Use (a − b)² = a² − 2ab + b² to find 59².
13. 13.Use a² − b² = (a + b)(a − b) to find 72² − 4².
14. 14.Use (a + b)² = a² + 2ab + b² to find 93².
15. 15.Find the value of x² + 2xy + y² when x = 4 and y = 1.
16. 16.Use (a + b)² = a² + 2ab + b² to find 39².
17. 17.Use (a + b)(a − b) = a² − b² to find 92 × 88.
18. 18.Use a² − b² = (a + b)(a − b) to find 73² − 7².
19. 19.Find the value of x² − y² when x = 5 and y = 4.
20. 20.If a − b = 6 and ab = 7, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 99² − 26².
22. 22.Use (a − b)² = a² − 2ab + b² to find 75².
23. 23.Use (a − b)² = a² − 2ab + b² to find 49².
24. 24.Use a² − b² = (a + b)(a − b) to find 25² − 9².
25. 25.Use (a − b)² = a² − 2ab + b² to find 12².
26. 26.Use (a + b)² = a² + 2ab + b² to find 73².
27. 27.Use (a + b)(a − b) = a² − b² to find 66 × 54.
28. 28.Find the value of x² + 2xy + y² when x = 3 and y = 2.
29. 29.Use (a − b)² = a² − 2ab + b² to find 42².
30. 30.Find the value of x² − y² when x = 7 and y = 4.
31. 31.Use a² − b² = (a + b)(a − b) to find 45² − 33².
32. 32.Use (a − b)² = a² − 2ab + b² to find 26².
33. 33.Use (a − b)² = a² − 2ab + b² to find 21².
34. 34.Use (a + b)² = a² + 2ab + b² to find 12².
35. 35.Use a² − b² = (a + b)(a − b) to find 31² − 19².
36. 36.Use (a + b)(a − b) = a² − b² to find 101 × 99.
37. 37.Find the value of x² + 2xy + y² when x = 10 and y = 3.
38. 38.If a + b = 14 and ab = 33, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 74² − 11².
40. 40.Use (a + b)² = a² + 2ab + b² to find 94².

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