Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 193 · 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 108 × 92.
2. 2.If a + b = 14 and ab = 40, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 89².
4. 4.If a + b = 6 and ab = 8, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 15².
6. 6.Use (a − b)² = a² − 2ab + b² to find 71².
7. 7.Use (a + b)(a − b) = a² − b² to find 38 × 22.
8. 8.Use (a + b)² = a² + 2ab + b² to find 32².
9. 9.If a − b = 2 and ab = 48, what is a² + b²?
10. 10.Find the value of x² − 2xy + y² when x = 13 and y = 8.
11. 11.If a − b = 1 and ab = 2, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 48 × 32.
13. 13.Find the value of x² − 2xy + y² when x = 4 and y = 3.
14. 14.If a + b = 7 and ab = 12, what is a² + b²?
15. 15.Find the value of x² − y² when x = 12 and y = 8.
16. 16.Use (a + b)² = a² + 2ab + b² to find 73².
17. 17.Use a² − b² = (a + b)(a − b) to find 63² − 35².
18. 18.If a + b = 3 and ab = 2, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 23².
20. 20.Use (a − b)² = a² − 2ab + b² to find 27².
21. 21.Use (a + b)² = a² + 2ab + b² to find 55².
22. 22.Use a² − b² = (a + b)(a − b) to find 24² − 5².
23. 23.Find the value of x² + 2xy + y² when x = 11 and y = 3.
24. 24.Use (a + b)² = a² + 2ab + b² to find 24².
25. 25.Use (a + b)² = a² + 2ab + b² to find 69².
26. 26.Use (a − b)² = a² − 2ab + b² to find 87².
27. 27.Use (a + b)(a − b) = a² − b² to find 91 × 89.
28. 28.Use (a + b)² = a² + 2ab + b² to find 47².
29. 29.Use a² − b² = (a + b)(a − b) to find 60² − 48².
30. 30.Use (a + b)(a − b) = a² − b² to find 67 × 53.
31. 31.Use a² − b² = (a + b)(a − b) to find 45² − 11².
32. 32.Use (a − b)² = a² − 2ab + b² to find 61².
33. 33.Use (a + b)² = a² + 2ab + b² to find 109².
34. 34.Use (a − b)² = a² − 2ab + b² to find 93².
35. 35.If a + b = 17 and ab = 70, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 75².
37. 37.Use (a + b)² = a² + 2ab + b² to find 51².
38. 38.Use a² − b² = (a + b)(a − b) to find 52² − 3².
39. 39.Use (a − b)² = a² − 2ab + b² to find 97².
40. 40.Use (a − b)² = a² − 2ab + b² to find 33².

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