Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 903 · 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 22².
2. 2.Use a² − b² = (a + b)(a − b) to find 32² − 9².
3. 3.Use (a − b)² = a² − 2ab + b² to find 98².
4. 4.Use (a − b)² = a² − 2ab + b² to find 31².
5. 5.Find the value of x² − 2xy + y² when x = 7 and y = 4.
6. 6.Use (a + b)(a − b) = a² − b² to find 63 × 57.
7. 7.Use a² − b² = (a + b)(a − b) to find 70² − 29².
8. 8.Use (a + b)² = a² + 2ab + b² to find 28².
9. 9.Use (a + b)(a − b) = a² − b² to find 21 × 19.
10. 10.If a + b = 12 and ab = 35, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 46 × 34.
12. 12.Use (a + b)² = a² + 2ab + b² to find 38².
13. 13.If a + b = 16 and ab = 63, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 41².
15. 15.If a + b = 4 and ab = 3, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 57².
17. 17.Use (a + b)(a − b) = a² − b² to find 72 × 68.
18. 18.Use (a + b)² = a² + 2ab + b² to find 101².
19. 19.If a − b = 1 and ab = 110, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 99².
21. 21.Use (a + b)(a − b) = a² − b² to find 82 × 78.
22. 22.Use a² − b² = (a + b)(a − b) to find 76² − 2².
23. 23.Use (a + b)² = a² + 2ab + b² to find 13².
24. 24.Use (a − b)² = a² − 2ab + b² to find 64².
25. 25.Use a² − b² = (a + b)(a − b) to find 45² − 12².
26. 26.Use (a + b)² = a² + 2ab + b² to find 36².
27. 27.Use a² − b² = (a + b)(a − b) to find 35² − 10².
28. 28.Use (a + b)² = a² + 2ab + b² to find 12².
29. 29.Use (a + b)(a − b) = a² − b² to find 77 × 63.
30. 30.Use (a − b)² = a² − 2ab + b² to find 37².
31. 31.If a − b = 3 and ab = 28, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 27² − 14².
33. 33.Use (a − b)² = a² − 2ab + b² to find 35².
34. 34.Find the value of x² + 2xy + y² when x = 4 and y = 3.
35. 35.Use (a + b)(a − b) = a² − b² to find 74 × 66.
36. 36.Use a² − b² = (a + b)(a − b) to find 40² − 14².
37. 37.Use (a + b)(a − b) = a² − b² to find 22 × 18.
38. 38.Use a² − b² = (a + b)(a − b) to find 74² − 6².
39. 39.If a + b = 8 and ab = 12, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 93 × 87.

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