Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 226 · 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 49 × 31.
2. 2.Use (a + b)(a − b) = a² − b² to find 75 × 65.
3. 3.If a − b = 2 and ab = 3, what is a² + b²?
4. 4.Use (a + b)(a − b) = a² − b² to find 61 × 59.
5. 5.If a − b = 10 and ab = 11, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 37 × 23.
7. 7.If a + b = 12 and ab = 27, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 61² − 22².
9. 9.Use (a − b)² = a² − 2ab + b² to find 93².
10. 10.Use (a + b)(a − b) = a² − b² to find 55 × 45.
11. 11.Use (a − b)² = a² − 2ab + b² to find 52².
12. 12.Use (a − b)² = a² − 2ab + b² to find 75².
13. 13.Use (a + b)(a − b) = a² − b² to find 41 × 39.
14. 14.Use (a + b)² = a² + 2ab + b² to find 101².
15. 15.Use (a − b)² = a² − 2ab + b² to find 23².
16. 16.Find the value of x² − y² when x = 5 and y = 1.
17. 17.Use (a + b)² = a² + 2ab + b² to find 26².
18. 18.Use a² − b² = (a + b)(a − b) to find 81² − 63².
19. 19.Use (a − b)² = a² − 2ab + b² to find 25².
20. 20.Use (a + b)² = a² + 2ab + b² to find 86².
21. 21.Use a² − b² = (a + b)(a − b) to find 76² − 53².
22. 22.Find the value of x² − 2xy + y² when x = 9 and y = 1.
23. 23.Use (a + b)(a − b) = a² − b² to find 38 × 22.
24. 24.Use a² − b² = (a + b)(a − b) to find 40² − 21².
25. 25.Use (a + b)(a − b) = a² − b² to find 47 × 33.
26. 26.If a − b = 1 and ab = 6, what is a² + b²?
27. 27.Use (a + b)² = a² + 2ab + b² to find 92².
28. 28.Find the value of x² − 2xy + y² when x = 6 and y = 2.
29. 29.Use (a + b)² = a² + 2ab + b² to find 24².
30. 30.Use (a + b)(a − b) = a² − b² to find 64 × 56.
31. 31.Use a² − b² = (a + b)(a − b) to find 55² − 34².
32. 32.If a + b = 17 and ab = 60, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 62² − 7².
34. 34.Use (a + b)² = a² + 2ab + b² to find 69².
35. 35.Use a² − b² = (a + b)(a − b) to find 35² − 17².
36. 36.Find the value of x² − 2xy + y² when x = 14 and y = 6.
37. 37.Use a² − b² = (a + b)(a − b) to find 28² − 25².
38. 38.Use (a + b)(a − b) = a² − b² to find 83 × 77.
39. 39.If a − b = 3 and ab = 40, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 67² − 2².

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