Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 237 · 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 99².
2. 2.Use (a + b)² = a² + 2ab + b² to find 39².
3. 3.Use (a + b)(a − b) = a² − b² to find 22 × 18.
4. 4.Use (a + b)² = a² + 2ab + b² to find 92².
5. 5.Use (a − b)² = a² − 2ab + b² to find 51².
6. 6.Use (a − b)² = a² − 2ab + b² to find 19².
7. 7.Use (a − b)² = a² − 2ab + b² to find 42².
8. 8.Find the value of x² + 2xy + y² when x = 9 and y = 4.
9. 9.Use (a + b)² = a² + 2ab + b² to find 66².
10. 10.Use (a − b)² = a² − 2ab + b² to find 15².
11. 11.Use (a + b)(a − b) = a² − b² to find 102 × 98.
12. 12.Use (a + b)(a − b) = a² − b² to find 71 × 69.
13. 13.Use (a + b)(a − b) = a² − b² to find 77 × 63.
14. 14.Use (a − b)² = a² − 2ab + b² to find 58².
15. 15.Use (a − b)² = a² − 2ab + b² to find 73².
16. 16.Use (a + b)² = a² + 2ab + b² to find 75².
17. 17.Find the value of x² − y² when x = 11 and y = 9.
18. 18.Use a² − b² = (a + b)(a − b) to find 32² − 11².
19. 19.If a + b = 3 and ab = 2, what is a² + b²?
20. 20.If a − b = 3 and ab = 40, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 47².
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 1.
23. 23.Use (a + b)² = a² + 2ab + b² to find 32².
24. 24.Use (a + b)² = a² + 2ab + b² to find 95².
25. 25.Use (a + b)(a − b) = a² − b² to find 105 × 95.
26. 26.Use (a − b)² = a² − 2ab + b² to find 93².
27. 27.Use (a + b)(a − b) = a² − b² to find 74 × 66.
28. 28.Use (a + b)(a − b) = a² − b² to find 81 × 79.
29. 29.Find the value of x² − 2xy + y² when x = 14 and y = 3.
30. 30.Use (a + b)(a − b) = a² − b² to find 39 × 21.
31. 31.Use (a + b)² = a² + 2ab + b² to find 69².
32. 32.Use (a − b)² = a² − 2ab + b² to find 67².
33. 33.Use (a + b)² = a² + 2ab + b² to find 64².
34. 34.Use (a + b)² = a² + 2ab + b² to find 19².
35. 35.If a + b = 5 and ab = 4, what is a² + b²?
36. 36.Use (a + b)(a − b) = a² − b² to find 29 × 11.
37. 37.Use (a + b)(a − b) = a² − b² to find 37 × 23.
38. 38.Use (a − b)² = a² − 2ab + b² to find 91².
39. 39.Use a² − b² = (a + b)(a − b) to find 68² − 18².
40. 40.If a + b = 12 and ab = 27, what is a² + b²?

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