Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 728 · 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)² = a² + 2ab + b² to find 56².
2. 2.Use (a + b)(a − b) = a² − b² to find 64 × 56.
3. 3.Use (a + b)² = a² + 2ab + b² to find 35².
4. 4.Use a² − b² = (a + b)(a − b) to find 85² − 67².
5. 5.Use (a − b)² = a² − 2ab + b² to find 76².
6. 6.If a − b = 4 and ab = 96, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 79².
8. 8.Use (a + b)(a − b) = a² − b² to find 108 × 92.
9. 9.Use a² − b² = (a + b)(a − b) to find 91² − 58².
10. 10.Find the value of x² + 2xy + y² when x = 3 and y = 2.
11. 11.Use (a − b)² = a² − 2ab + b² to find 13².
12. 12.Use (a + b)(a − b) = a² − b² to find 25 × 15.
13. 13.Use (a − b)² = a² − 2ab + b² to find 68².
14. 14.Use (a + b)² = a² + 2ab + b² to find 15².
15. 15.Use (a + b)(a − b) = a² − b² to find 85 × 75.
16. 16.Use (a + b)(a − b) = a² − b² to find 46 × 34.
17. 17.Use (a + b)² = a² + 2ab + b² to find 93².
18. 18.Use (a + b)(a − b) = a² − b² to find 87 × 73.
19. 19.Find the value of x² + 2xy + y² when x = 5 and y = 2.
20. 20.Use a² − b² = (a + b)(a − b) to find 21² − 19².
21. 21.If a − b = 5 and ab = 24, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 28².
23. 23.If a − b = 6 and ab = 7, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 11².
25. 25.Use (a − b)² = a² − 2ab + b² to find 32².
26. 26.Use (a − b)² = a² − 2ab + b² to find 59².
27. 27.Use (a − b)² = a² − 2ab + b² to find 29².
28. 28.Use (a + b)(a − b) = a² − b² to find 35 × 25.
29. 29.Use (a − b)² = a² − 2ab + b² to find 94².
30. 30.Use (a + b)(a − b) = a² − b² to find 73 × 67.
31. 31.Use a² − b² = (a + b)(a − b) to find 23² − 13².
32. 32.Find the value of x² + 2xy + y² when x = 9 and y = 4.
33. 33.Use (a + b)² = a² + 2ab + b² to find 53².
34. 34.Use (a − b)² = a² − 2ab + b² to find 17².
35. 35.Use (a + b)² = a² + 2ab + b² to find 26².
36. 36.Use (a + b)² = a² + 2ab + b² to find 68².
37. 37.Use (a + b)(a − b) = a² − b² to find 28 × 12.
38. 38.Use a² − b² = (a + b)(a − b) to find 42² − 26².
39. 39.If a − b = 8 and ab = 20, what is a² + b²?
40. 40.Find the value of x² − y² when x = 5 and y = 4.

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