Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 894 · 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 102².
2. 2.If a + b = 3 and ab = 2, what is a² + b²?
3. 3.Use (a + b)(a − b) = a² − b² to find 76 × 64.
4. 4.Use (a + b)² = a² + 2ab + b² to find 28².
5. 5.Use (a − b)² = a² − 2ab + b² to find 57².
6. 6.Use (a + b)(a − b) = a² − b² to find 106 × 94.
7. 7.Find the value of x² + 2xy + y² when x = 6 and y = 2.
8. 8.Use (a + b)(a − b) = a² − b² to find 46 × 34.
9. 9.Use (a + b)(a − b) = a² − b² to find 66 × 54.
10. 10.Find the value of x² − y² when x = 6 and y = 2.
11. 11.Use (a − b)² = a² − 2ab + b² to find 76².
12. 12.Use (a + b)² = a² + 2ab + b² to find 37².
13. 13.Use (a + b)² = a² + 2ab + b² to find 85².
14. 14.If a + b = 7 and ab = 10, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 18².
16. 16.Use a² − b² = (a + b)(a − b) to find 32² − 7².
17. 17.Find the value of x² − 2xy + y² when x = 4 and y = 2.
18. 18.Use (a + b)(a − b) = a² − b² to find 22 × 18.
19. 19.Use (a − b)² = a² − 2ab + b² to find 88².
20. 20.Use (a − b)² = a² − 2ab + b² to find 22².
21. 21.Use (a + b)(a − b) = a² − b² to find 21 × 19.
22. 22.If a − b = 5 and ab = 6, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 43².
24. 24.If a + b = 17 and ab = 70, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 36².
26. 26.Use a² − b² = (a + b)(a − b) to find 25² − 10².
27. 27.Use (a − b)² = a² − 2ab + b² to find 66².
28. 28.Use (a − b)² = a² − 2ab + b² to find 12².
29. 29.Use (a + b)(a − b) = a² − b² to find 82 × 78.
30. 30.Use (a − b)² = a² − 2ab + b² to find 68².
31. 31.Use (a + b)(a − b) = a² − b² to find 55 × 45.
32. 32.Use a² − b² = (a + b)(a − b) to find 33² − 10².
33. 33.Use (a − b)² = a² − 2ab + b² to find 99².
34. 34.Use (a + b)(a − b) = a² − b² to find 95 × 85.
35. 35.Use (a + b)² = a² + 2ab + b² to find 81².
36. 36.If a − b = 1 and ab = 6, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 49².
38. 38.Find the value of x² − y² when x = 6 and y = 1.
39. 39.Use (a + b)² = a² + 2ab + b² to find 88².
40. 40.Find the value of x² + 2xy + y² when x = 6 and y = 4.

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