Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 239 · 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 48².
2. 2.Use (a + b)(a − b) = a² − b² to find 44 × 36.
3. 3.Use (a − b)² = a² − 2ab + b² to find 27².
4. 4.Use (a + b)² = a² + 2ab + b² to find 37².
5. 5.Use (a + b)² = a² + 2ab + b² to find 66².
6. 6.Use (a + b)² = a² + 2ab + b² to find 11².
7. 7.Use a² − b² = (a + b)(a − b) to find 75² − 31².
8. 8.Use (a + b)(a − b) = a² − b² to find 27 × 13.
9. 9.If a − b = 9 and ab = 22, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 39 × 21.
11. 11.Use (a − b)² = a² − 2ab + b² to find 61².
12. 12.Use (a + b)² = a² + 2ab + b² to find 22².
13. 13.Use (a − b)² = a² − 2ab + b² to find 68².
14. 14.Use (a − b)² = a² − 2ab + b² to find 23².
15. 15.Use (a + b)² = a² + 2ab + b² to find 53².
16. 16.If a − b = 1 and ab = 2, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 97 × 83.
18. 18.Use a² − b² = (a + b)(a − b) to find 31² − 12².
19. 19.Use a² − b² = (a + b)(a − b) to find 64² − 11².
20. 20.Use (a − b)² = a² − 2ab + b² to find 19².
21. 21.If a − b = 3 and ab = 70, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 73 × 67.
23. 23.Use (a − b)² = a² − 2ab + b² to find 53².
24. 24.Find the value of x² + 2xy + y² when x = 5 and y = 3.
25. 25.If a − b = 5 and ab = 84, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 37² − 14².
27. 27.Use (a + b)(a − b) = a² − b² to find 31 × 29.
28. 28.Use (a + b)² = a² + 2ab + b² to find 52².
29. 29.Use (a + b)² = a² + 2ab + b² to find 106².
30. 30.Use a² − b² = (a + b)(a − b) to find 55² − 36².
31. 31.Use a² − b² = (a + b)(a − b) to find 80² − 26².
32. 32.Use (a − b)² = a² − 2ab + b² to find 57².
33. 33.Find the value of x² − 2xy + y² when x = 9 and y = 3.
34. 34.If a + b = 15 and ab = 54, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 47 × 33.
36. 36.Find the value of x² + 2xy + y² when x = 15 and y = 13.
37. 37.Use (a + b)² = a² + 2ab + b² to find 32².
38. 38.Use (a − b)² = a² − 2ab + b² to find 76².
39. 39.If a − b = 4 and ab = 5, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 91² − 41².

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