Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 812 · 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.If a − b = 2 and ab = 15, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 71² − 59².
3. 3.Use (a + b)² = a² + 2ab + b² to find 16².
4. 4.Use (a + b)(a − b) = a² − b² to find 74 × 66.
5. 5.Use (a + b)(a − b) = a² − b² to find 29 × 11.
6. 6.If a + b = 5 and ab = 6, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 82² − 73².
8. 8.Use a² − b² = (a + b)(a − b) to find 62² − 24².
9. 9.Use a² − b² = (a + b)(a − b) to find 29² − 28².
10. 10.Use a² − b² = (a + b)(a − b) to find 59² − 25².
11. 11.Find the value of x² + 2xy + y² when x = 6 and y = 3.
12. 12.Find the value of x² + 2xy + y² when x = 5 and y = 1.
13. 13.Use (a + b)² = a² + 2ab + b² to find 81².
14. 14.Find the value of x² − y² when x = 8 and y = 3.
15. 15.Use (a − b)² = a² − 2ab + b² to find 39².
16. 16.Use (a − b)² = a² − 2ab + b² to find 17².
17. 17.Use a² − b² = (a + b)(a − b) to find 29² − 5².
18. 18.Use a² − b² = (a + b)(a − b) to find 82² − 37².
19. 19.Use (a − b)² = a² − 2ab + b² to find 27².
20. 20.If a + b = 11 and ab = 18, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 42².
22. 22.If a + b = 4 and ab = 3, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 73².
24. 24.If a + b = 12 and ab = 32, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 88 × 72.
26. 26.Find the value of x² − 2xy + y² when x = 9 and y = 3.
27. 27.Use (a + b)(a − b) = a² − b² to find 85 × 75.
28. 28.Use (a + b)² = a² + 2ab + b² to find 95².
29. 29.Use (a + b)(a − b) = a² − b² to find 108 × 92.
30. 30.Use (a + b)(a − b) = a² − b² to find 106 × 94.
31. 31.Use (a + b)² = a² + 2ab + b² to find 54².
32. 32.Find the value of x² − y² when x = 11 and y = 2.
33. 33.Use (a + b)² = a² + 2ab + b² to find 53².
34. 34.If a − b = 9 and ab = 10, what is a² + b²?
35. 35.If a + b = 9 and ab = 20, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 11².
37. 37.Use (a + b)(a − b) = a² − b² to find 91 × 89.
38. 38.Use (a − b)² = a² − 2ab + b² to find 14².
39. 39.If a + b = 8 and ab = 12, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 78².

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