Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 837 · 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 = 1 and ab = 132, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 72².
3. 3.Use (a + b)² = a² + 2ab + b² to find 91².
4. 4.Use a² − b² = (a + b)(a − b) to find 48² − 25².
5. 5.Use a² − b² = (a + b)(a − b) to find 56² − 16².
6. 6.Use (a + b)² = a² + 2ab + b² to find 32².
7. 7.Find the value of x² − y² when x = 12 and y = 3.
8. 8.Use a² − b² = (a + b)(a − b) to find 27² − 18².
9. 9.Use (a + b)(a − b) = a² − b² to find 67 × 53.
10. 10.If a − b = 1 and ab = 30, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 51² − 34².
12. 12.Use (a − b)² = a² − 2ab + b² to find 76².
13. 13.Use (a + b)² = a² + 2ab + b² to find 29².
14. 14.Use (a + b)² = a² + 2ab + b² to find 26².
15. 15.Use (a + b)² = a² + 2ab + b² to find 51².
16. 16.Use (a + b)² = a² + 2ab + b² to find 22².
17. 17.Use (a + b)² = a² + 2ab + b² to find 95².
18. 18.Use (a + b)(a − b) = a² − b² to find 91 × 89.
19. 19.Use (a + b)² = a² + 2ab + b² to find 76².
20. 20.Use (a + b)(a − b) = a² − b² to find 32 × 28.
21. 21.Use a² − b² = (a + b)(a − b) to find 98² − 7².
22. 22.If a + b = 11 and ab = 30, what is a² + b²?
23. 23.Use (a + b)² = a² + 2ab + b² to find 11².
24. 24.Use (a − b)² = a² − 2ab + b² to find 24².
25. 25.If a − b = 3 and ab = 28, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 29².
27. 27.Use (a + b)(a − b) = a² − b² to find 22 × 18.
28. 28.Use (a − b)² = a² − 2ab + b² to find 19².
29. 29.Use a² − b² = (a + b)(a − b) to find 24² − 11².
30. 30.Use (a + b)(a − b) = a² − b² to find 105 × 95.
31. 31.If a + b = 15 and ab = 56, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 36² − 35².
33. 33.If a + b = 3 and ab = 2, what is a² + b²?
34. 34.If a + b = 4 and ab = 3, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 98² − 77².
36. 36.Use (a + b)² = a² + 2ab + b² to find 17².
37. 37.Use (a + b)(a − b) = a² − b² to find 93 × 87.
38. 38.Use (a − b)² = a² − 2ab + b² to find 59².
39. 39.Find the value of x² + 2xy + y² when x = 3 and y = 1.
40. 40.Use (a + b)(a − b) = a² − b² to find 27 × 13.

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