Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 782 · 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 59² − 14².
2. 2.Use a² − b² = (a + b)(a − b) to find 32² − 19².
3. 3.Find the value of x² − y² when x = 3 and y = 1.
4. 4.Use (a − b)² = a² − 2ab + b² to find 54².
5. 5.Use (a − b)² = a² − 2ab + b² to find 28².
6. 6.Use (a + b)(a − b) = a² − b² to find 61 × 59.
7. 7.Find the value of x² + 2xy + y² when x = 8 and y = 4.
8. 8.Use (a + b)(a − b) = a² − b² to find 93 × 87.
9. 9.Find the value of x² − y² when x = 4 and y = 1.
10. 10.Use a² − b² = (a + b)(a − b) to find 40² − 30².
11. 11.Find the value of x² − y² when x = 4 and y = 2.
12. 12.Use (a + b)(a − b) = a² − b² to find 25 × 15.
13. 13.Use (a − b)² = a² − 2ab + b² to find 99².
14. 14.Use (a + b)(a − b) = a² − b² to find 59 × 41.
15. 15.Use (a − b)² = a² − 2ab + b² to find 38².
16. 16.Use (a − b)² = a² − 2ab + b² to find 12².
17. 17.Find the value of x² + 2xy + y² when x = 9 and y = 8.
18. 18.Find the value of x² + 2xy + y² when x = 9 and y = 3.
19. 19.Use (a + b)² = a² + 2ab + b² to find 76².
20. 20.Use (a + b)² = a² + 2ab + b² to find 106².
21. 21.If a + b = 11 and ab = 28, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 75 × 65.
23. 23.Use (a + b)(a − b) = a² − b² to find 92 × 88.
24. 24.Use (a − b)² = a² − 2ab + b² to find 74².
25. 25.Use (a + b)² = a² + 2ab + b² to find 45².
26. 26.Use (a + b)(a − b) = a² − b² to find 78 × 62.
27. 27.Use a² − b² = (a + b)(a − b) to find 70² − 69².
28. 28.Use a² − b² = (a + b)(a − b) to find 20² − 7².
29. 29.Use (a + b)(a − b) = a² − b² to find 39 × 21.
30. 30.Use (a + b)(a − b) = a² − b² to find 81 × 79.
31. 31.Use a² − b² = (a + b)(a − b) to find 48² − 22².
32. 32.Use (a − b)² = a² − 2ab + b² to find 14².
33. 33.Use (a + b)² = a² + 2ab + b² to find 82².
34. 34.Use a² − b² = (a + b)(a − b) to find 99² − 23².
35. 35.Use (a + b)² = a² + 2ab + b² to find 41².
36. 36.Use (a + b)(a − b) = a² − b² to find 108 × 92.
37. 37.Use (a − b)² = a² − 2ab + b² to find 95².
38. 38.Find the value of x² − 2xy + y² when x = 4 and y = 2.
39. 39.Use (a + b)² = a² + 2ab + b² to find 22².
40. 40.If a + b = 3 and ab = 2, what is a² + b²?

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