Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 643 · 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 = 8, what is a² + b²?
2. 2.Find the value of x² + 2xy + y² when x = 15 and y = 9.
3. 3.If a − b = 1 and ab = 2, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 48².
5. 5.Use (a − b)² = a² − 2ab + b² to find 31².
6. 6.Use (a + b)(a − b) = a² − b² to find 39 × 21.
7. 7.If a + b = 10 and ab = 16, what is a² + b²?
8. 8.If a − b = 1 and ab = 6, what is a² + b²?
9. 9.If a − b = 6 and ab = 27, what is a² + b²?
10. 10.If a + b = 13 and ab = 40, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 52².
12. 12.Find the value of x² + 2xy + y² when x = 3 and y = 1.
13. 13.Use (a − b)² = a² − 2ab + b² to find 15².
14. 14.Use (a + b)² = a² + 2ab + b² to find 61².
15. 15.If a + b = 11 and ab = 18, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 51².
17. 17.Use (a − b)² = a² − 2ab + b² to find 34².
18. 18.Use (a + b)² = a² + 2ab + b² to find 18².
19. 19.Use (a + b)(a − b) = a² − b² to find 21 × 19.
20. 20.If a + b = 9 and ab = 18, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 76² − 40².
22. 22.Use (a − b)² = a² − 2ab + b² to find 27².
23. 23.Use (a + b)² = a² + 2ab + b² to find 94².
24. 24.Use (a + b)² = a² + 2ab + b² to find 56².
25. 25.Use a² − b² = (a + b)(a − b) to find 71² − 47².
26. 26.Use (a + b)² = a² + 2ab + b² to find 72².
27. 27.Use (a − b)² = a² − 2ab + b² to find 13².
28. 28.Find the value of x² − y² when x = 5 and y = 1.
29. 29.Find the value of x² − 2xy + y² when x = 4 and y = 3.
30. 30.Use (a + b)(a − b) = a² − b² to find 33 × 27.
31. 31.Use (a + b)² = a² + 2ab + b² to find 84².
32. 32.Use (a + b)(a − b) = a² − b² to find 24 × 16.
33. 33.Use (a − b)² = a² − 2ab + b² to find 35².
34. 34.Use (a − b)² = a² − 2ab + b² to find 22².
35. 35.Use a² − b² = (a + b)(a − b) to find 34² − 18².
36. 36.If a − b = 2 and ab = 48, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 55².
38. 38.If a − b = 4 and ab = 5, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 96².
40. 40.Use a² − b² = (a + b)(a − b) to find 91² − 38².

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