Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 46 · 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 83².
2. 2.Use (a + b)(a − b) = a² − b² to find 38 × 22.
3. 3.Use (a − b)² = a² − 2ab + b² to find 71².
4. 4.Use (a + b)² = a² + 2ab + b² to find 15².
5. 5.If a + b = 6 and ab = 8, what is a² + b²?
6. 6.If a + b = 3 and ab = 2, what is a² + b²?
7. 7.Find the value of x² + 2xy + y² when x = 15 and y = 14.
8. 8.Use a² − b² = (a + b)(a − b) to find 81² − 56².
9. 9.Find the value of x² + 2xy + y² when x = 4 and y = 1.
10. 10.Use a² − b² = (a + b)(a − b) to find 60² − 57².
11. 11.Use (a + b)(a − b) = a² − b² to find 44 × 36.
12. 12.Find the value of x² + 2xy + y² when x = 5 and y = 1.
13. 13.Use (a + b)² = a² + 2ab + b² to find 39².
14. 14.Use (a + b)(a − b) = a² − b² to find 27 × 13.
15. 15.Use (a + b)(a − b) = a² − b² to find 43 × 37.
16. 16.Use (a + b)² = a² + 2ab + b² to find 89².
17. 17.Use (a − b)² = a² − 2ab + b² to find 23².
18. 18.Use (a + b)² = a² + 2ab + b² to find 95².
19. 19.Use (a − b)² = a² − 2ab + b² to find 77².
20. 20.If a − b = 3 and ab = 4, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 50² − 19².
22. 22.Use a² − b² = (a + b)(a − b) to find 24² − 4².
23. 23.Use (a − b)² = a² − 2ab + b² to find 58².
24. 24.Use a² − b² = (a + b)(a − b) to find 75² − 47².
25. 25.Use a² − b² = (a + b)(a − b) to find 21² − 12².
26. 26.Use (a − b)² = a² − 2ab + b² to find 97².
27. 27.Use (a − b)² = a² − 2ab + b² to find 28².
28. 28.If a − b = 1 and ab = 56, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 42².
30. 30.Use (a − b)² = a² − 2ab + b² to find 15².
31. 31.Use (a + b)² = a² + 2ab + b² to find 94².
32. 32.Use (a − b)² = a² − 2ab + b² to find 61².
33. 33.Use (a + b)² = a² + 2ab + b² to find 69².
34. 34.Use a² − b² = (a + b)(a − b) to find 81² − 37².
35. 35.Find the value of x² − y² when x = 11 and y = 4.
36. 36.Use (a + b)(a − b) = a² − b² to find 22 × 18.
37. 37.If a − b = 2 and ab = 35, what is a² + b²?
38. 38.If a + b = 4 and ab = 3, what is a² + b²?
39. 39.Find the value of x² + 2xy + y² when x = 7 and y = 2.
40. 40.If a + b = 7 and ab = 12, what is a² + b²?

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