Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 312 · 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.If a − b = 7 and ab = 8, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 27².
3. 3.Use (a + b)(a − b) = a² − b² to find 87 × 73.
4. 4.Find the value of x² + 2xy + y² when x = 12 and y = 2.
5. 5.Find the value of x² − y² when x = 7 and y = 6.
6. 6.Use a² − b² = (a + b)(a − b) to find 45² − 18².
7. 7.Use (a + b)² = a² + 2ab + b² to find 17².
8. 8.Use (a + b)² = a² + 2ab + b² to find 21².
9. 9.Use (a + b)² = a² + 2ab + b² to find 92².
10. 10.Use (a + b)² = a² + 2ab + b² to find 59².
11. 11.Use (a − b)² = a² − 2ab + b² to find 56².
12. 12.Use (a − b)² = a² − 2ab + b² to find 48².
13. 13.If a + b = 17 and ab = 72, what is a² + b²?
14. 14.If a − b = 4 and ab = 32, what is a² + b²?
15. 15.If a − b = 9 and ab = 10, what is a² + b²?
16. 16.Find the value of x² − y² when x = 4 and y = 3.
17. 17.Use a² − b² = (a + b)(a − b) to find 44² − 35².
18. 18.Use (a + b)(a − b) = a² − b² to find 49 × 31.
19. 19.If a − b = 1 and ab = 6, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 68².
21. 21.Find the value of x² − 2xy + y² when x = 9 and y = 1.
22. 22.Use (a − b)² = a² − 2ab + b² to find 51².
23. 23.Find the value of x² − 2xy + y² when x = 13 and y = 7.
24. 24.Use (a + b)² = a² + 2ab + b² to find 56².
25. 25.Use (a + b)² = a² + 2ab + b² to find 89².
26. 26.Use (a − b)² = a² − 2ab + b² to find 11².
27. 27.If a − b = 4 and ab = 5, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 89² − 35².
29. 29.Use a² − b² = (a + b)(a − b) to find 73² − 25².
30. 30.If a + b = 3 and ab = 2, what is a² + b²?
31. 31.Find the value of x² − y² when x = 11 and y = 3.
32. 32.Use (a + b)² = a² + 2ab + b² to find 15².
33. 33.Use a² − b² = (a + b)(a − b) to find 83² − 76².
34. 34.Use a² − b² = (a + b)(a − b) to find 22² − 4².
35. 35.If a + b = 11 and ab = 28, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 29² − 1².
37. 37.If a + b = 11 and ab = 10, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 98².
39. 39.Use (a + b)² = a² + 2ab + b² to find 63².
40. 40.Use (a + b)(a − b) = a² − b² to find 103 × 97.

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