Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 379 · 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.Find the value of x² − y² when x = 3 and y = 1.
2. 2.Use (a + b)(a − b) = a² − b² to find 42 × 38.
3. 3.If a + b = 9 and ab = 8, what is a² + b²?
4. 4.If a + b = 4 and ab = 3, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 25².
6. 6.Use (a + b)² = a² + 2ab + b² to find 63².
7. 7.Use a² − b² = (a + b)(a − b) to find 26² − 7².
8. 8.Use (a − b)² = a² − 2ab + b² to find 47².
9. 9.Use (a + b)(a − b) = a² − b² to find 82 × 78.
10. 10.Use (a + b)² = a² + 2ab + b² to find 93².
11. 11.Use (a − b)² = a² − 2ab + b² to find 45².
12. 12.Use (a − b)² = a² − 2ab + b² to find 95².
13. 13.Use a² − b² = (a + b)(a − b) to find 93² − 19².
14. 14.Use (a + b)(a − b) = a² − b² to find 84 × 76.
15. 15.If a − b = 6 and ab = 55, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 69².
17. 17.Use (a + b)² = a² + 2ab + b² to find 65².
18. 18.Use (a − b)² = a² − 2ab + b² to find 26².
19. 19.Use a² − b² = (a + b)(a − b) to find 53² − 6².
20. 20.If a + b = 5 and ab = 4, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 107 × 93.
22. 22.Use (a − b)² = a² − 2ab + b² to find 33².
23. 23.Use (a − b)² = a² − 2ab + b² to find 96².
24. 24.Use (a + b)(a − b) = a² − b² to find 105 × 95.
25. 25.Use (a + b)(a − b) = a² − b² to find 86 × 74.
26. 26.Find the value of x² − y² when x = 5 and y = 1.
27. 27.Use (a − b)² = a² − 2ab + b² to find 14².
28. 28.If a − b = 1 and ab = 20, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 61².
30. 30.Use a² − b² = (a + b)(a − b) to find 99² − 74².
31. 31.If a − b = 7 and ab = 30, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 77 × 63.
33. 33.Use (a + b)(a − b) = a² − b² to find 63 × 57.
34. 34.Use (a + b)² = a² + 2ab + b² to find 47².
35. 35.If a + b = 17 and ab = 70, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 49².
37. 37.Use (a + b)(a − b) = a² − b² to find 103 × 97.
38. 38.Find the value of x² + 2xy + y² when x = 3 and y = 1.
39. 39.Find the value of x² − y² when x = 11 and y = 1.
40. 40.If a + b = 13 and ab = 30, what is a² + b²?

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