Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 56 · 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 101².
2. 2.Use a² − b² = (a + b)(a − b) to find 52² − 31².
3. 3.Use a² − b² = (a + b)(a − b) to find 23² − 18².
4. 4.If a − b = 2 and ab = 63, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 66².
6. 6.Use (a + b)(a − b) = a² − b² to find 57 × 43.
7. 7.Use (a − b)² = a² − 2ab + b² to find 93².
8. 8.If a − b = 1 and ab = 6, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 45 × 35.
10. 10.Use (a − b)² = a² − 2ab + b² to find 71².
11. 11.Use (a + b)² = a² + 2ab + b² to find 24².
12. 12.Find the value of x² − 2xy + y² when x = 9 and y = 8.
13. 13.If a + b = 3 and ab = 2, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 52².
15. 15.Use (a + b)² = a² + 2ab + b² to find 63².
16. 16.If a + b = 4 and ab = 3, what is a² + b²?
17. 17.Find the value of x² + 2xy + y² when x = 9 and y = 6.
18. 18.Use a² − b² = (a + b)(a − b) to find 26² − 19².
19. 19.Use (a + b)² = a² + 2ab + b² to find 36².
20. 20.Use (a − b)² = a² − 2ab + b² to find 57².
21. 21.Use (a + b)(a − b) = a² − b² to find 72 × 68.
22. 22.Use (a + b)(a − b) = a² − b² to find 82 × 78.
23. 23.Find the value of x² + 2xy + y² when x = 10 and y = 9.
24. 24.If a + b = 5 and ab = 4, what is a² + b²?
25. 25.If a − b = 4 and ab = 5, what is a² + b²?
26. 26.Find the value of x² − y² when x = 10 and y = 7.
27. 27.Find the value of x² − y² when x = 8 and y = 5.
28. 28.Use (a − b)² = a² − 2ab + b² to find 65².
29. 29.Use (a − b)² = a² − 2ab + b² to find 34².
30. 30.Use (a + b)² = a² + 2ab + b² to find 43².
31. 31.Use (a + b)(a − b) = a² − b² to find 92 × 88.
32. 32.Use (a + b)² = a² + 2ab + b² to find 102².
33. 33.Use (a − b)² = a² − 2ab + b² to find 75².
34. 34.Use (a + b)² = a² + 2ab + b² to find 88².
35. 35.Find the value of x² − y² when x = 4 and y = 3.
36. 36.If a − b = 1 and ab = 2, what is a² + b²?
37. 37.Use (a + b)(a − b) = a² − b² to find 32 × 28.
38. 38.If a + b = 12 and ab = 32, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 51².
40. 40.Use a² − b² = (a + b)(a − b) to find 52² − 2².

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