Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 888 · 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 103².
2. 2.Use (a − b)² = a² − 2ab + b² to find 86².
3. 3.Use a² − b² = (a + b)(a − b) to find 32² − 6².
4. 4.Use (a − b)² = a² − 2ab + b² to find 45².
5. 5.If a + b = 3 and ab = 2, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 64².
7. 7.Use (a + b)(a − b) = a² − b² to find 25 × 15.
8. 8.Use (a + b)² = a² + 2ab + b² to find 43².
9. 9.Use (a + b)(a − b) = a² − b² to find 23 × 17.
10. 10.Use (a + b)(a − b) = a² − b² to find 58 × 42.
11. 11.Use (a − b)² = a² − 2ab + b² to find 37².
12. 12.Use (a + b)² = a² + 2ab + b² to find 86².
13. 13.Use a² − b² = (a + b)(a − b) to find 87² − 51².
14. 14.Use (a − b)² = a² − 2ab + b² to find 56².
15. 15.Use a² − b² = (a + b)(a − b) to find 22² − 17².
16. 16.Use (a + b)² = a² + 2ab + b² to find 61².
17. 17.Find the value of x² + 2xy + y² when x = 9 and y = 7.
18. 18.Use a² − b² = (a + b)(a − b) to find 29² − 3².
19. 19.Find the value of x² + 2xy + y² when x = 15 and y = 12.
20. 20.Use (a + b)² = a² + 2ab + b² to find 98².
21. 21.Find the value of x² − y² when x = 6 and y = 1.
22. 22.If a − b = 3 and ab = 88, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 22².
24. 24.Use (a + b)² = a² + 2ab + b² to find 87².
25. 25.If a + b = 9 and ab = 20, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 18².
27. 27.Use a² − b² = (a + b)(a − b) to find 20² − 6².
28. 28.Use (a + b)² = a² + 2ab + b² to find 62².
29. 29.Use (a + b)(a − b) = a² − b² to find 95 × 85.
30. 30.Use a² − b² = (a + b)(a − b) to find 46² − 12².
31. 31.Use (a + b)(a − b) = a² − b² to find 36 × 24.
32. 32.Find the value of x² + 2xy + y² when x = 3 and y = 1.
33. 33.Find the value of x² − y² when x = 3 and y = 2.
34. 34.Use (a + b)² = a² + 2ab + b² to find 48².
35. 35.Use a² − b² = (a + b)(a − b) to find 39² − 24².
36. 36.If a + b = 15 and ab = 36, what is a² + b²?
37. 37.If a + b = 14 and ab = 33, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 82².
39. 39.Use (a + b)² = a² + 2ab + b² to find 12².
40. 40.Use (a − b)² = a² − 2ab + b² to find 58².

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