Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 21 · 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 = 8 and ab = 12, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 105².
3. 3.Find the value of x² + 2xy + y² when x = 5 and y = 1.
4. 4.Use (a + b)(a − b) = a² − b² to find 79 × 61.
5. 5.Use (a + b)² = a² + 2ab + b² to find 78².
6. 6.Use (a + b)² = a² + 2ab + b² to find 84².
7. 7.Use (a + b)(a − b) = a² − b² to find 94 × 86.
8. 8.Use a² − b² = (a + b)(a − b) to find 49² − 32².
9. 9.If a + b = 11 and ab = 18, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 29² − 11².
11. 11.Use (a + b)² = a² + 2ab + b² to find 94².
12. 12.Use (a + b)² = a² + 2ab + b² to find 99².
13. 13.If a + b = 3 and ab = 2, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 54².
15. 15.Use (a + b)² = a² + 2ab + b² to find 12².
16. 16.Use (a − b)² = a² − 2ab + b² to find 97².
17. 17.Use (a + b)(a − b) = a² − b² to find 41 × 39.
18. 18.Use a² − b² = (a + b)(a − b) to find 85² − 13².
19. 19.Find the value of x² + 2xy + y² when x = 7 and y = 3.
20. 20.If a + b = 13 and ab = 12, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 19².
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 6.
23. 23.Use (a − b)² = a² − 2ab + b² to find 41².
24. 24.If a − b = 4 and ab = 32, what is a² + b²?
25. 25.If a − b = 2 and ab = 24, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 56 × 44.
27. 27.If a + b = 14 and ab = 33, what is a² + b²?
28. 28.If a − b = 3 and ab = 88, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 66².
30. 30.If a − b = 1 and ab = 56, what is a² + b²?
31. 31.If a + b = 9 and ab = 8, what is a² + b²?
32. 32.If a + b = 4 and ab = 3, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 98² − 41².
34. 34.Use a² − b² = (a + b)(a − b) to find 55² − 27².
35. 35.Use (a + b)(a − b) = a² − b² to find 45 × 35.
36. 36.Find the value of x² − 2xy + y² when x = 7 and y = 1.
37. 37.Find the value of x² + 2xy + y² when x = 4 and y = 2.
38. 38.Use (a + b)² = a² + 2ab + b² to find 62².
39. 39.Find the value of x² − y² when x = 15 and y = 2.
40. 40.Use (a + b)(a − b) = a² − b² to find 31 × 29.

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