Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 683 · 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 29 × 11.
2. 2.Find the value of x² − y² when x = 11 and y = 7.
3. 3.Find the value of x² + 2xy + y² when x = 6 and y = 5.
4. 4.Use (a − b)² = a² − 2ab + b² to find 93².
5. 5.Use a² − b² = (a + b)(a − b) to find 49² − 2².
6. 6.Find the value of x² − 2xy + y² when x = 4 and y = 3.
7. 7.Find the value of x² − y² when x = 4 and y = 3.
8. 8.Use (a + b)(a − b) = a² − b² to find 107 × 93.
9. 9.If a + b = 10 and ab = 9, what is a² + b²?
10. 10.If a − b = 3 and ab = 4, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 47 × 33.
12. 12.Find the value of x² − y² when x = 11 and y = 4.
13. 13.Use a² − b² = (a + b)(a − b) to find 67² − 61².
14. 14.Use (a + b)² = a² + 2ab + b² to find 13².
15. 15.Use (a + b)² = a² + 2ab + b² to find 91².
16. 16.Use a² − b² = (a + b)(a − b) to find 41² − 6².
17. 17.If a − b = 1 and ab = 6, what is a² + b²?
18. 18.Use (a − b)² = a² − 2ab + b² to find 29².
19. 19.Use (a + b)² = a² + 2ab + b² to find 96².
20. 20.Use (a + b)(a − b) = a² − b² to find 28 × 12.
21. 21.Use (a + b)² = a² + 2ab + b² to find 106².
22. 22.Use (a + b)(a − b) = a² − b² to find 25 × 15.
23. 23.Use (a + b)² = a² + 2ab + b² to find 42².
24. 24.Use (a − b)² = a² − 2ab + b² to find 58².
25. 25.Use a² − b² = (a + b)(a − b) to find 66² − 42².
26. 26.Use (a + b)(a − b) = a² − b² to find 79 × 61.
27. 27.Find the value of x² − 2xy + y² when x = 7 and y = 5.
28. 28.Use (a + b)² = a² + 2ab + b² to find 12².
29. 29.Use (a + b)² = a² + 2ab + b² to find 15².
30. 30.Find the value of x² + 2xy + y² when x = 8 and y = 2.
31. 31.Find the value of x² + 2xy + y² when x = 9 and y = 6.
32. 32.Use (a + b)² = a² + 2ab + b² to find 33².
33. 33.Find the value of x² + 2xy + y² when x = 12 and y = 1.
34. 34.Use (a − b)² = a² − 2ab + b² to find 76².
35. 35.Use (a − b)² = a² − 2ab + b² to find 66².
36. 36.Use (a + b)(a − b) = a² − b² to find 53 × 47.
37. 37.Use a² − b² = (a + b)(a − b) to find 27² − 15².
38. 38.If a − b = 7 and ab = 30, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 38².
40. 40.Find the value of x² − y² when x = 3 and y = 2.

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