Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 37 · 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)(a − b) = a² − b² to find 63 × 57.
2. 2.Use (a + b)² = a² + 2ab + b² to find 64².
3. 3.Find the value of x² − y² when x = 3 and y = 1.
4. 4.Use (a + b)² = a² + 2ab + b² to find 49².
5. 5.Use (a − b)² = a² − 2ab + b² to find 34².
6. 6.Find the value of x² − 2xy + y² when x = 7 and y = 5.
7. 7.Use (a + b)² = a² + 2ab + b² to find 106².
8. 8.Use (a − b)² = a² − 2ab + b² to find 23².
9. 9.Use (a − b)² = a² − 2ab + b² to find 24².
10. 10.Use (a + b)(a − b) = a² − b² to find 78 × 62.
11. 11.Use (a + b)(a − b) = a² − b² to find 93 × 87.
12. 12.Use (a + b)(a − b) = a² − b² to find 83 × 77.
13. 13.Use (a − b)² = a² − 2ab + b² to find 54².
14. 14.Use (a + b)² = a² + 2ab + b² to find 66².
15. 15.Use (a − b)² = a² − 2ab + b² to find 94².
16. 16.Use (a + b)² = a² + 2ab + b² to find 72².
17. 17.If a + b = 5 and ab = 6, what is a² + b²?
18. 18.If a + b = 13 and ab = 30, what is a² + b²?
19. 19.Use (a − b)² = a² − 2ab + b² to find 15².
20. 20.Use a² − b² = (a + b)(a − b) to find 45² − 6².
21. 21.Find the value of x² + 2xy + y² when x = 15 and y = 11.
22. 22.Use (a + b)(a − b) = a² − b² to find 37 × 23.
23. 23.Use (a + b)² = a² + 2ab + b² to find 35².
24. 24.If a − b = 1 and ab = 2, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 23² − 9².
26. 26.Find the value of x² − y² when x = 7 and y = 4.
27. 27.Use a² − b² = (a + b)(a − b) to find 43² − 23².
28. 28.Use a² − b² = (a + b)(a − b) to find 83² − 30².
29. 29.Find the value of x² − y² when x = 13 and y = 7.
30. 30.Use (a + b)(a − b) = a² − b² to find 47 × 33.
31. 31.Use a² − b² = (a + b)(a − b) to find 87² − 65².
32. 32.Use (a + b)² = a² + 2ab + b² to find 13².
33. 33.Use (a + b)(a − b) = a² − b² to find 96 × 84.
34. 34.Use (a + b)(a − b) = a² − b² to find 107 × 93.
35. 35.Use (a + b)(a − b) = a² − b² to find 28 × 12.
36. 36.Find the value of x² − y² when x = 5 and y = 4.
37. 37.Use (a − b)² = a² − 2ab + b² to find 52².
38. 38.Use (a − b)² = a² − 2ab + b² to find 11².
39. 39.Use (a − b)² = a² − 2ab + b² to find 26².
40. 40.Use (a + b)² = a² + 2ab + b² to find 17².

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