Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 519 · 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 26².
2. 2.Use (a + b)² = a² + 2ab + b² to find 55².
3. 3.Use a² − b² = (a + b)(a − b) to find 76² − 17².
4. 4.Use a² − b² = (a + b)(a − b) to find 28² − 15².
5. 5.Use (a − b)² = a² − 2ab + b² to find 24².
6. 6.Use a² − b² = (a + b)(a − b) to find 39² − 38².
7. 7.Use a² − b² = (a + b)(a − b) to find 77² − 64².
8. 8.If a − b = 2 and ab = 48, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 63².
10. 10.Find the value of x² − y² when x = 4 and y = 1.
11. 11.Find the value of x² + 2xy + y² when x = 9 and y = 5.
12. 12.Use a² − b² = (a + b)(a − b) to find 46² − 11².
13. 13.If a + b = 7 and ab = 6, what is a² + b²?
14. 14.Find the value of x² − y² when x = 10 and y = 8.
15. 15.Use a² − b² = (a + b)(a − b) to find 46² − 39².
16. 16.If a + b = 7 and ab = 12, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 25² − 5².
18. 18.Use (a + b)² = a² + 2ab + b² to find 93².
19. 19.Find the value of x² + 2xy + y² when x = 3 and y = 2.
20. 20.Use a² − b² = (a + b)(a − b) to find 92² − 65².
21. 21.Use (a − b)² = a² − 2ab + b² to find 68².
22. 22.Use (a + b)(a − b) = a² − b² to find 35 × 25.
23. 23.Use (a + b)(a − b) = a² − b² to find 97 × 83.
24. 24.Find the value of x² − y² when x = 11 and y = 2.
25. 25.If a − b = 2 and ab = 24, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 96².
27. 27.If a + b = 9 and ab = 18, what is a² + b²?
28. 28.If a + b = 14 and ab = 45, what is a² + b²?
29. 29.Find the value of x² − y² when x = 12 and y = 9.
30. 30.Use a² − b² = (a + b)(a − b) to find 33² − 23².
31. 31.Use (a + b)² = a² + 2ab + b² to find 101².
32. 32.Use (a + b)² = a² + 2ab + b² to find 97².
33. 33.Use (a + b)(a − b) = a² − b² to find 23 × 17.
34. 34.Use (a + b)(a − b) = a² − b² to find 92 × 88.
35. 35.Use (a + b)² = a² + 2ab + b² to find 84².
36. 36.Find the value of x² − y² when x = 13 and y = 12.
37. 37.Use (a + b)(a − b) = a² − b² to find 33 × 27.
38. 38.If a + b = 20 and ab = 96, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 48² − 3².
40. 40.Use (a + b)² = a² + 2ab + b² to find 109².

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