Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 417 · 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 41².
2. 2.If a − b = 7 and ab = 60, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 91 × 89.
4. 4.Find the value of x² + 2xy + y² when x = 5 and y = 2.
5. 5.Use (a + b)(a − b) = a² − b² to find 89 × 71.
6. 6.If a − b = 10 and ab = 24, what is a² + b²?
7. 7.Find the value of x² − y² when x = 11 and y = 9.
8. 8.Find the value of x² − y² when x = 5 and y = 1.
9. 9.Use (a − b)² = a² − 2ab + b² to find 42².
10. 10.Use (a + b)(a − b) = a² − b² to find 35 × 25.
11. 11.Use (a − b)² = a² − 2ab + b² to find 18².
12. 12.Use (a − b)² = a² − 2ab + b² to find 22².
13. 13.Use a² − b² = (a + b)(a − b) to find 80² − 43².
14. 14.Use (a + b)² = a² + 2ab + b² to find 28².
15. 15.Use (a − b)² = a² − 2ab + b² to find 11².
16. 16.Find the value of x² − y² when x = 6 and y = 5.
17. 17.Use a² − b² = (a + b)(a − b) to find 64² − 27².
18. 18.Use (a + b)² = a² + 2ab + b² to find 96².
19. 19.Use (a + b)² = a² + 2ab + b² to find 34².
20. 20.Use (a + b)² = a² + 2ab + b² to find 85².
21. 21.If a + b = 5 and ab = 6, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 54 × 46.
23. 23.Use (a − b)² = a² − 2ab + b² to find 25².
24. 24.Find the value of x² − 2xy + y² when x = 11 and y = 10.
25. 25.Use (a − b)² = a² − 2ab + b² to find 75².
26. 26.Use (a + b)² = a² + 2ab + b² to find 22².
27. 27.Use (a + b)² = a² + 2ab + b² to find 38².
28. 28.Use (a + b)² = a² + 2ab + b² to find 14².
29. 29.If a − b = 2 and ab = 24, what is a² + b²?
30. 30.If a + b = 14 and ab = 33, what is a² + b²?
31. 31.Find the value of x² + 2xy + y² when x = 6 and y = 2.
32. 32.If a + b = 21 and ab = 108, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 83² − 26².
34. 34.Use a² − b² = (a + b)(a − b) to find 27² − 9².
35. 35.Use (a + b)² = a² + 2ab + b² to find 82².
36. 36.Use a² − b² = (a + b)(a − b) to find 90² − 34².
37. 37.Use (a + b)(a − b) = a² − b² to find 81 × 79.
38. 38.Use (a + b)(a − b) = a² − b² to find 44 × 36.
39. 39.Use a² − b² = (a + b)(a − b) to find 65² − 15².
40. 40.Use a² − b² = (a + b)(a − b) to find 64² − 53².

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