Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 639 · 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 73 × 67.
2. 2.Use (a + b)(a − b) = a² − b² to find 71 × 69.
3. 3.Use (a + b)(a − b) = a² − b² to find 26 × 14.
4. 4.Use (a + b)² = a² + 2ab + b² to find 11².
5. 5.Use a² − b² = (a + b)(a − b) to find 36² − 18².
6. 6.Find the value of x² − 2xy + y² when x = 6 and y = 1.
7. 7.Use (a + b)(a − b) = a² − b² to find 45 × 35.
8. 8.Use (a + b)² = a² + 2ab + b² to find 22².
9. 9.Use (a + b)² = a² + 2ab + b² to find 75².
10. 10.Use (a − b)² = a² − 2ab + b² to find 98².
11. 11.Use (a + b)² = a² + 2ab + b² to find 105².
12. 12.Use a² − b² = (a + b)(a − b) to find 99² − 90².
13. 13.Find the value of x² − 2xy + y² when x = 9 and y = 6.
14. 14.Use (a + b)² = a² + 2ab + b² to find 38².
15. 15.Use (a − b)² = a² − 2ab + b² to find 36².
16. 16.Use (a − b)² = a² − 2ab + b² to find 79².
17. 17.Use (a − b)² = a² − 2ab + b² to find 15².
18. 18.Use (a + b)(a − b) = a² − b² to find 95 × 85.
19. 19.Use (a + b)² = a² + 2ab + b² to find 14².
20. 20.Use (a + b)² = a² + 2ab + b² to find 73².
21. 21.Use (a − b)² = a² − 2ab + b² to find 32².
22. 22.Find the value of x² + 2xy + y² when x = 6 and y = 3.
23. 23.Use (a − b)² = a² − 2ab + b² to find 23².
24. 24.Find the value of x² − y² when x = 13 and y = 5.
25. 25.If a − b = 1 and ab = 30, what is a² + b²?
26. 26.If a − b = 3 and ab = 88, what is a² + b²?
27. 27.If a − b = 5 and ab = 66, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 74 × 66.
29. 29.Find the value of x² + 2xy + y² when x = 14 and y = 12.
30. 30.Use (a − b)² = a² − 2ab + b² to find 77².
31. 31.Use (a + b)² = a² + 2ab + b² to find 77².
32. 32.Find the value of x² − 2xy + y² when x = 8 and y = 1.
33. 33.Use (a − b)² = a² − 2ab + b² to find 44².
34. 34.Use a² − b² = (a + b)(a − b) to find 84² − 64².
35. 35.Use (a + b)² = a² + 2ab + b² to find 26².
36. 36.If a − b = 1 and ab = 2, what is a² + b²?
37. 37.If a − b = 5 and ab = 24, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 69².
39. 39.Use (a + b)² = a² + 2ab + b² to find 13².
40. 40.Use (a − b)² = a² − 2ab + b² to find 33².

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