Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 942 · 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 62².
2. 2.Use (a + b)(a − b) = a² − b² to find 64 × 56.
3. 3.Use (a + b)² = a² + 2ab + b² to find 22².
4. 4.If a − b = 7 and ab = 30, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 12².
6. 6.If a + b = 16 and ab = 48, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 91².
8. 8.Use a² − b² = (a + b)(a − b) to find 41² − 25².
9. 9.Use a² − b² = (a + b)(a − b) to find 79² − 4².
10. 10.Find the value of x² − y² when x = 6 and y = 5.
11. 11.Use (a + b)(a − b) = a² − b² to find 105 × 95.
12. 12.Use a² − b² = (a + b)(a − b) to find 73² − 63².
13. 13.Use (a + b)² = a² + 2ab + b² to find 92².
14. 14.Use (a − b)² = a² − 2ab + b² to find 61².
15. 15.Use (a + b)(a − b) = a² − b² to find 95 × 85.
16. 16.Use (a − b)² = a² − 2ab + b² to find 33².
17. 17.Use (a − b)² = a² − 2ab + b² to find 53².
18. 18.Find the value of x² − y² when x = 15 and y = 13.
19. 19.Use (a − b)² = a² − 2ab + b² to find 51².
20. 20.If a − b = 1 and ab = 12, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 78².
22. 22.If a + b = 3 and ab = 2, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 43².
24. 24.If a + b = 10 and ab = 16, what is a² + b²?
25. 25.Use a² − b² = (a + b)(a − b) to find 83² − 34².
26. 26.Find the value of x² − 2xy + y² when x = 14 and y = 2.
27. 27.Use a² − b² = (a + b)(a − b) to find 53² − 22².
28. 28.Find the value of x² − y² when x = 10 and y = 1.
29. 29.Use a² − b² = (a + b)(a − b) to find 39² − 21².
30. 30.If a + b = 5 and ab = 4, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 36².
32. 32.Use a² − b² = (a + b)(a − b) to find 65² − 33².
33. 33.Use (a − b)² = a² − 2ab + b² to find 73².
34. 34.Use (a − b)² = a² − 2ab + b² to find 83².
35. 35.If a + b = 13 and ab = 30, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 39 × 21.
37. 37.Use (a − b)² = a² − 2ab + b² to find 87².
38. 38.Use (a − b)² = a² − 2ab + b² to find 39².
39. 39.Use (a − b)² = a² − 2ab + b² to find 11².
40. 40.Use (a + b)² = a² + 2ab + b² to find 67².

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