Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 7 · 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 = 15 and ab = 50, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 88².
3. 3.Find the value of x² − y² when x = 6 and y = 3.
4. 4.Use (a + b)² = a² + 2ab + b² to find 35².
5. 5.Find the value of x² + 2xy + y² when x = 8 and y = 2.
6. 6.If a − b = 8 and ab = 9, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 69 × 51.
8. 8.If a + b = 12 and ab = 32, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 63 × 57.
10. 10.Use (a − b)² = a² − 2ab + b² to find 86².
11. 11.Use (a + b)² = a² + 2ab + b² to find 38².
12. 12.If a − b = 4 and ab = 5, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 31².
14. 14.If a + b = 3 and ab = 2, what is a² + b²?
15. 15.Find the value of x² + 2xy + y² when x = 5 and y = 1.
16. 16.Use a² − b² = (a + b)(a − b) to find 53² − 4².
17. 17.Use a² − b² = (a + b)(a − b) to find 31² − 18².
18. 18.Use (a + b)² = a² + 2ab + b² to find 68².
19. 19.If a + b = 11 and ab = 30, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 11².
21. 21.Use a² − b² = (a + b)(a − b) to find 86² − 83².
22. 22.Find the value of x² − 2xy + y² when x = 11 and y = 6.
23. 23.Use (a + b)(a − b) = a² − b² to find 32 × 28.
24. 24.Use (a + b)² = a² + 2ab + b² to find 82².
25. 25.Use (a + b)² = a² + 2ab + b² to find 49².
26. 26.Use (a + b)(a − b) = a² − b² to find 65 × 55.
27. 27.Use (a + b)² = a² + 2ab + b² to find 61².
28. 28.Use (a − b)² = a² − 2ab + b² to find 48².
29. 29.Use a² − b² = (a + b)(a − b) to find 81² − 36².
30. 30.Use (a − b)² = a² − 2ab + b² to find 23².
31. 31.Find the value of x² − y² when x = 6 and y = 1.
32. 32.Use (a + b)(a − b) = a² − b² to find 85 × 75.
33. 33.Use (a + b)(a − b) = a² − b² to find 61 × 59.
34. 34.Use (a + b)² = a² + 2ab + b² to find 88².
35. 35.If a − b = 6 and ab = 16, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 102 × 98.
37. 37.Use a² − b² = (a + b)(a − b) to find 63² − 20².
38. 38.Use (a − b)² = a² − 2ab + b² to find 91².
39. 39.If a − b = 1 and ab = 12, what is a² + b²?
40. 40.If a + b = 5 and ab = 6, what is a² + b²?

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