Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 153 · 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)(a − b) = a² − b² to find 34 × 26.
2. 2.Use a² − b² = (a + b)(a − b) to find 20² − 8².
3. 3.Find the value of x² + 2xy + y² when x = 14 and y = 8.
4. 4.Use (a + b)(a − b) = a² − b² to find 61 × 59.
5. 5.Use (a − b)² = a² − 2ab + b² to find 17².
6. 6.Use (a − b)² = a² − 2ab + b² to find 45².
7. 7.Use (a + b)² = a² + 2ab + b² to find 46².
8. 8.Use a² − b² = (a + b)(a − b) to find 26² − 11².
9. 9.Use (a − b)² = a² − 2ab + b² to find 58².
10. 10.Find the value of x² − y² when x = 15 and y = 10.
11. 11.Use a² − b² = (a + b)(a − b) to find 70² − 21².
12. 12.Use (a − b)² = a² − 2ab + b² to find 78².
13. 13.Use (a − b)² = a² − 2ab + b² to find 11².
14. 14.Use (a + b)² = a² + 2ab + b² to find 61².
15. 15.If a − b = 1 and ab = 6, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 106 × 94.
17. 17.Use (a − b)² = a² − 2ab + b² to find 46².
18. 18.Use (a − b)² = a² − 2ab + b² to find 37².
19. 19.Find the value of x² − 2xy + y² when x = 4 and y = 2.
20. 20.Use (a − b)² = a² − 2ab + b² to find 57².
21. 21.Find the value of x² + 2xy + y² when x = 9 and y = 8.
22. 22.Use (a + b)² = a² + 2ab + b² to find 108².
23. 23.Use a² − b² = (a + b)(a − b) to find 72² − 56².
24. 24.Use a² − b² = (a + b)(a − b) to find 87² − 82².
25. 25.Use (a + b)(a − b) = a² − b² to find 35 × 25.
26. 26.Use (a + b)(a − b) = a² − b² to find 87 × 73.
27. 27.Use a² − b² = (a + b)(a − b) to find 36² − 11².
28. 28.If a + b = 10 and ab = 21, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 73².
30. 30.Use (a + b)² = a² + 2ab + b² to find 64².
31. 31.Use (a − b)² = a² − 2ab + b² to find 32².
32. 32.Use a² − b² = (a + b)(a − b) to find 58² − 53².
33. 33.Use a² − b² = (a + b)(a − b) to find 31² − 22².
34. 34.Use a² − b² = (a + b)(a − b) to find 25² − 1².
35. 35.Find the value of x² − 2xy + y² when x = 15 and y = 2.
36. 36.Use (a + b)(a − b) = a² − b² to find 44 × 36.
37. 37.Use (a + b)(a − b) = a² − b² to find 82 × 78.
38. 38.Find the value of x² − y² when x = 3 and y = 1.
39. 39.Use (a + b)² = a² + 2ab + b² to find 39².
40. 40.Use (a + b)² = a² + 2ab + b² to find 23².

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