Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 263 · 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 a² − b² = (a + b)(a − b) to find 83² − 23².
2. 2.Find the value of x² + 2xy + y² when x = 3 and y = 1.
3. 3.Find the value of x² − y² when x = 8 and y = 5.
4. 4.Use (a + b)(a − b) = a² − b² to find 23 × 17.
5. 5.Use (a + b)(a − b) = a² − b² to find 76 × 64.
6. 6.Use (a − b)² = a² − 2ab + b² to find 19².
7. 7.Use a² − b² = (a + b)(a − b) to find 43² − 11².
8. 8.Use a² − b² = (a + b)(a − b) to find 54² − 13².
9. 9.If a + b = 18 and ab = 80, what is a² + b²?
10. 10.Use (a + b)² = a² + 2ab + b² to find 38².
11. 11.Use (a − b)² = a² − 2ab + b² to find 27².
12. 12.Use a² − b² = (a + b)(a − b) to find 64² − 52².
13. 13.Use (a + b)² = a² + 2ab + b² to find 25².
14. 14.Use a² − b² = (a + b)(a − b) to find 88² − 2².
15. 15.Use (a − b)² = a² − 2ab + b² to find 84².
16. 16.Use (a + b)² = a² + 2ab + b² to find 17².
17. 17.Find the value of x² − 2xy + y² when x = 11 and y = 8.
18. 18.Use (a + b)(a − b) = a² − b² to find 81 × 79.
19. 19.Use (a − b)² = a² − 2ab + b² to find 56².
20. 20.Use (a − b)² = a² − 2ab + b² to find 35².
21. 21.Use (a + b)² = a² + 2ab + b² to find 39².
22. 22.Use (a + b)(a − b) = a² − b² to find 43 × 37.
23. 23.Use a² − b² = (a + b)(a − b) to find 86² − 36².
24. 24.Use a² − b² = (a + b)(a − b) to find 65² − 31².
25. 25.Use (a + b)² = a² + 2ab + b² to find 41².
26. 26.If a + b = 5 and ab = 4, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 76² − 34².
28. 28.Use (a + b)² = a² + 2ab + b² to find 14².
29. 29.Find the value of x² + 2xy + y² when x = 14 and y = 5.
30. 30.Use (a + b)(a − b) = a² − b² to find 58 × 42.
31. 31.Use (a − b)² = a² − 2ab + b² to find 45².
32. 32.Find the value of x² − 2xy + y² when x = 6 and y = 5.
33. 33.If a + b = 11 and ab = 28, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 92 × 88.
35. 35.Use (a − b)² = a² − 2ab + b² to find 49².
36. 36.Use a² − b² = (a + b)(a − b) to find 70² − 65².
37. 37.Use (a + b)² = a² + 2ab + b² to find 102².
38. 38.Use (a + b)(a − b) = a² − b² to find 71 × 69.
39. 39.Use (a + b)(a − b) = a² − b² to find 56 × 44.
40. 40.Use (a + b)(a − b) = a² − b² to find 61 × 59.

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