Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 298 · 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 91².
2. 2.Use (a − b)² = a² − 2ab + b² to find 84².
3. 3.Use (a − b)² = a² − 2ab + b² to find 14².
4. 4.If a − b = 2 and ab = 3, what is a² + b²?
5. 5.Use (a + b)(a − b) = a² − b² to find 54 × 46.
6. 6.Use a² − b² = (a + b)(a − b) to find 40² − 6².
7. 7.Find the value of x² + 2xy + y² when x = 6 and y = 4.
8. 8.Use (a − b)² = a² − 2ab + b² to find 27².
9. 9.Use (a + b)(a − b) = a² − b² to find 89 × 71.
10. 10.Use a² − b² = (a + b)(a − b) to find 44² − 9².
11. 11.Use (a + b)² = a² + 2ab + b² to find 53².
12. 12.Find the value of x² − y² when x = 12 and y = 6.
13. 13.If a + b = 15 and ab = 44, what is a² + b²?
14. 14.If a + b = 20 and ab = 99, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 22².
16. 16.If a + b = 12 and ab = 32, what is a² + b²?
17. 17.If a − b = 10 and ab = 24, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 70² − 59².
19. 19.Use a² − b² = (a + b)(a − b) to find 73² − 35².
20. 20.If a − b = 4 and ab = 5, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 38 × 22.
22. 22.Use (a − b)² = a² − 2ab + b² to find 74².
23. 23.Use (a + b)(a − b) = a² − b² to find 105 × 95.
24. 24.If a + b = 7 and ab = 12, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 85 × 75.
26. 26.Use a² − b² = (a + b)(a − b) to find 33² − 15².
27. 27.Use (a + b)(a − b) = a² − b² to find 87 × 73.
28. 28.Use (a − b)² = a² − 2ab + b² to find 99².
29. 29.Use (a + b)² = a² + 2ab + b² to find 93².
30. 30.Use (a + b)² = a² + 2ab + b² to find 81².
31. 31.Use (a + b)² = a² + 2ab + b² to find 21².
32. 32.Use a² − b² = (a + b)(a − b) to find 63² − 28².
33. 33.Find the value of x² − 2xy + y² when x = 12 and y = 11.
34. 34.Use a² − b² = (a + b)(a − b) to find 86² − 75².
35. 35.Use (a + b)(a − b) = a² − b² to find 95 × 85.
36. 36.Use (a − b)² = a² − 2ab + b² to find 18².
37. 37.Use (a − b)² = a² − 2ab + b² to find 28².
38. 38.If a + b = 12 and ab = 27, what is a² + b²?
39. 39.Find the value of x² + 2xy + y² when x = 8 and y = 1.
40. 40.If a + b = 5 and ab = 6, what is a² + b²?

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