Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 763 · 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 47².
2. 2.If a + b = 8 and ab = 15, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 20² − 15².
4. 4.Use (a + b)² = a² + 2ab + b² to find 24².
5. 5.Use (a + b)² = a² + 2ab + b² to find 26².
6. 6.If a − b = 4 and ab = 5, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 61².
8. 8.If a + b = 10 and ab = 9, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 23².
10. 10.Use a² − b² = (a + b)(a − b) to find 36² − 1².
11. 11.Use (a − b)² = a² − 2ab + b² to find 93².
12. 12.Use (a + b)² = a² + 2ab + b² to find 11².
13. 13.Use (a + b)(a − b) = a² − b² to find 43 × 37.
14. 14.If a − b = 5 and ab = 50, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 41².
16. 16.If a + b = 15 and ab = 54, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 64² − 49².
18. 18.If a − b = 7 and ab = 30, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 71².
20. 20.Use (a + b)(a − b) = a² − b² to find 53 × 47.
21. 21.Use (a + b)² = a² + 2ab + b² to find 41².
22. 22.If a + b = 3 and ab = 2, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 72 × 68.
24. 24.If a − b = 6 and ab = 7, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 27².
26. 26.Use (a + b)(a − b) = a² − b² to find 66 × 54.
27. 27.Find the value of x² − y² when x = 14 and y = 13.
28. 28.Find the value of x² − 2xy + y² when x = 4 and y = 2.
29. 29.Use (a + b)(a − b) = a² − b² to find 79 × 61.
30. 30.Use (a + b)² = a² + 2ab + b² to find 49².
31. 31.Find the value of x² − y² when x = 15 and y = 9.
32. 32.Use (a + b)² = a² + 2ab + b² to find 19².
33. 33.Use (a + b)(a − b) = a² − b² to find 26 × 14.
34. 34.Use (a + b)(a − b) = a² − b² to find 23 × 17.
35. 35.Use (a + b)(a − b) = a² − b² to find 39 × 21.
36. 36.Use (a + b)² = a² + 2ab + b² to find 62².
37. 37.Use (a − b)² = a² − 2ab + b² to find 16².
38. 38.If a − b = 1 and ab = 72, what is a² + b²?
39. 39.Find the value of x² + 2xy + y² when x = 5 and y = 4.
40. 40.Use (a + b)(a − b) = a² − b² to find 52 × 48.

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