Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 715 · 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 49² − 38².
2. 2.Use (a + b)² = a² + 2ab + b² to find 53².
3. 3.Find the value of x² − 2xy + y² when x = 10 and y = 5.
4. 4.If a + b = 3 and ab = 2, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 24².
6. 6.Use (a + b)(a − b) = a² − b² to find 93 × 87.
7. 7.Use a² − b² = (a + b)(a − b) to find 56² − 27².
8. 8.If a − b = 2 and ab = 3, what is a² + b²?
9. 9.Use (a − b)² = a² − 2ab + b² to find 54².
10. 10.Use (a + b)² = a² + 2ab + b² to find 34².
11. 11.Use (a + b)² = a² + 2ab + b² to find 86².
12. 12.Use (a + b)(a − b) = a² − b² to find 108 × 92.
13. 13.Use (a + b)² = a² + 2ab + b² to find 29².
14. 14.Use (a − b)² = a² − 2ab + b² to find 25².
15. 15.If a − b = 1 and ab = 12, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 22².
17. 17.Use a² − b² = (a + b)(a − b) to find 77² − 23².
18. 18.Use (a + b)² = a² + 2ab + b² to find 81².
19. 19.Find the value of x² − 2xy + y² when x = 13 and y = 4.
20. 20.Use a² − b² = (a + b)(a − b) to find 72² − 33².
21. 21.Use (a + b)(a − b) = a² − b² to find 47 × 33.
22. 22.Use (a − b)² = a² − 2ab + b² to find 63².
23. 23.If a + b = 11 and ab = 30, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 15².
25. 25.Use (a − b)² = a² − 2ab + b² to find 98².
26. 26.Use (a + b)² = a² + 2ab + b² to find 42².
27. 27.If a − b = 1 and ab = 30, what is a² + b²?
28. 28.Find the value of x² − y² when x = 8 and y = 1.
29. 29.Use (a + b)² = a² + 2ab + b² to find 16².
30. 30.Find the value of x² − y² when x = 15 and y = 2.
31. 31.Use (a + b)² = a² + 2ab + b² to find 101².
32. 32.Use a² − b² = (a + b)(a − b) to find 55² − 18².
33. 33.Find the value of x² − 2xy + y² when x = 15 and y = 2.
34. 34.If a − b = 2 and ab = 35, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 89 × 71.
36. 36.Use (a + b)(a − b) = a² − b² to find 59 × 41.
37. 37.Find the value of x² − y² when x = 15 and y = 11.
38. 38.If a − b = 1 and ab = 56, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 17².
40. 40.Use (a − b)² = a² − 2ab + b² to find 39².

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