Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 985 · 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 103 × 97.
2. 2.Use a² − b² = (a + b)(a − b) to find 64² − 50².
3. 3.If a + b = 9 and ab = 14, what is a² + b²?
4. 4.If a + b = 5 and ab = 6, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 101².
6. 6.Use (a − b)² = a² − 2ab + b² to find 96².
7. 7.Use (a + b)² = a² + 2ab + b² to find 83².
8. 8.Use (a + b)² = a² + 2ab + b² to find 45².
9. 9.Use (a − b)² = a² − 2ab + b² to find 66².
10. 10.If a − b = 2 and ab = 8, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 73².
12. 12.Find the value of x² − 2xy + y² when x = 14 and y = 1.
13. 13.Use a² − b² = (a + b)(a − b) to find 70² − 21².
14. 14.Use (a + b)² = a² + 2ab + b² to find 39².
15. 15.Use a² − b² = (a + b)(a − b) to find 52² − 46².
16. 16.Use a² − b² = (a + b)(a − b) to find 88² − 36².
17. 17.Find the value of x² − y² when x = 11 and y = 1.
18. 18.Find the value of x² − 2xy + y² when x = 6 and y = 2.
19. 19.Use a² − b² = (a + b)(a − b) to find 47² − 3².
20. 20.Use (a − b)² = a² − 2ab + b² to find 55².
21. 21.If a − b = 5 and ab = 24, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 11².
23. 23.Use (a + b)(a − b) = a² − b² to find 76 × 64.
24. 24.Use (a + b)² = a² + 2ab + b² to find 21².
25. 25.If a − b = 4 and ab = 5, what is a² + b²?
26. 26.Find the value of x² + 2xy + y² when x = 8 and y = 7.
27. 27.Use (a − b)² = a² − 2ab + b² to find 57².
28. 28.Use (a + b)(a − b) = a² − b² to find 72 × 68.
29. 29.Find the value of x² + 2xy + y² when x = 4 and y = 2.
30. 30.Use a² − b² = (a + b)(a − b) to find 63² − 43².
31. 31.Use (a − b)² = a² − 2ab + b² to find 52².
32. 32.Use a² − b² = (a + b)(a − b) to find 54² − 20².
33. 33.Find the value of x² − y² when x = 15 and y = 11.
34. 34.Use (a + b)² = a² + 2ab + b² to find 15².
35. 35.Find the value of x² + 2xy + y² when x = 10 and y = 6.
36. 36.Use (a − b)² = a² − 2ab + b² to find 36².
37. 37.If a + b = 7 and ab = 6, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 23 × 17.
39. 39.Use a² − b² = (a + b)(a − b) to find 27² − 19².
40. 40.Use (a − b)² = a² − 2ab + b² to find 14².

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