Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 638 · 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 52 × 48.
2. 2.Use (a − b)² = a² − 2ab + b² to find 53².
3. 3.Use (a − b)² = a² − 2ab + b² to find 26².
4. 4.Use (a + b)(a − b) = a² − b² to find 22 × 18.
5. 5.Use (a + b)(a − b) = a² − b² to find 58 × 42.
6. 6.Use (a − b)² = a² − 2ab + b² to find 27².
7. 7.Use (a − b)² = a² − 2ab + b² to find 35².
8. 8.Use a² − b² = (a + b)(a − b) to find 96² − 53².
9. 9.Use a² − b² = (a + b)(a − b) to find 49² − 27².
10. 10.Use (a − b)² = a² − 2ab + b² to find 14².
11. 11.Use (a + b)² = a² + 2ab + b² to find 76².
12. 12.Use a² − b² = (a + b)(a − b) to find 59² − 12².
13. 13.Use (a + b)(a − b) = a² − b² to find 95 × 85.
14. 14.Use a² − b² = (a + b)(a − b) to find 58² − 8².
15. 15.Use (a + b)(a − b) = a² − b² to find 103 × 97.
16. 16.Use a² − b² = (a + b)(a − b) to find 69² − 12².
17. 17.Use (a + b)² = a² + 2ab + b² to find 103².
18. 18.Use (a + b)² = a² + 2ab + b² to find 79².
19. 19.Use a² − b² = (a + b)(a − b) to find 49² − 40².
20. 20.Use (a + b)(a − b) = a² − b² to find 63 × 57.
21. 21.Find the value of x² + 2xy + y² when x = 12 and y = 4.
22. 22.Use (a − b)² = a² − 2ab + b² to find 19².
23. 23.If a + b = 4 and ab = 3, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 21².
25. 25.If a − b = 1 and ab = 30, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 98².
27. 27.Find the value of x² − y² when x = 8 and y = 3.
28. 28.Use (a − b)² = a² − 2ab + b² to find 11².
29. 29.Use (a + b)² = a² + 2ab + b² to find 31².
30. 30.Use (a + b)² = a² + 2ab + b² to find 26².
31. 31.Find the value of x² + 2xy + y² when x = 3 and y = 2.
32. 32.Use (a − b)² = a² − 2ab + b² to find 77².
33. 33.If a − b = 1 and ab = 2, what is a² + b²?
34. 34.If a + b = 10 and ab = 16, what is a² + b²?
35. 35.Find the value of x² − y² when x = 3 and y = 2.
36. 36.Use a² − b² = (a + b)(a − b) to find 54² − 42².
37. 37.Use (a + b)(a − b) = a² − b² to find 68 × 52.
38. 38.Find the value of x² + 2xy + y² when x = 4 and y = 2.
39. 39.Use a² − b² = (a + b)(a − b) to find 93² − 32².
40. 40.Find the value of x² − y² when x = 13 and y = 3.

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