Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 240 · 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 63².
2. 2.Use a² − b² = (a + b)(a − b) to find 45² − 13².
3. 3.Use a² − b² = (a + b)(a − b) to find 76² − 1².
4. 4.If a − b = 4 and ab = 5, what is a² + b²?
5. 5.If a + b = 3 and ab = 2, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 64² − 48².
7. 7.Use (a − b)² = a² − 2ab + b² to find 45².
8. 8.Find the value of x² − y² when x = 6 and y = 2.
9. 9.Find the value of x² − y² when x = 8 and y = 5.
10. 10.Use (a + b)² = a² + 2ab + b² to find 91².
11. 11.Use (a − b)² = a² − 2ab + b² to find 56².
12. 12.Find the value of x² + 2xy + y² when x = 10 and y = 1.
13. 13.Find the value of x² − y² when x = 7 and y = 2.
14. 14.If a − b = 6 and ab = 27, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 58².
16. 16.Use (a + b)² = a² + 2ab + b² to find 42².
17. 17.Use (a + b)² = a² + 2ab + b² to find 28².
18. 18.Find the value of x² − y² when x = 3 and y = 2.
19. 19.Use a² − b² = (a + b)(a − b) to find 36² − 27².
20. 20.If a + b = 10 and ab = 24, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 38².
22. 22.Find the value of x² + 2xy + y² when x = 12 and y = 6.
23. 23.Use (a + b)(a − b) = a² − b² to find 41 × 39.
24. 24.If a − b = 8 and ab = 9, what is a² + b²?
25. 25.Use (a + b)² = a² + 2ab + b² to find 102².
26. 26.Find the value of x² − 2xy + y² when x = 12 and y = 2.
27. 27.Use (a − b)² = a² − 2ab + b² to find 41².
28. 28.Use (a + b)² = a² + 2ab + b² to find 72².
29. 29.Use (a − b)² = a² − 2ab + b² to find 67².
30. 30.Use (a + b)(a − b) = a² − b² to find 89 × 71.
31. 31.Use a² − b² = (a + b)(a − b) to find 73² − 10².
32. 32.Use (a + b)² = a² + 2ab + b² to find 56².
33. 33.Use (a + b)(a − b) = a² − b² to find 42 × 38.
34. 34.Find the value of x² + 2xy + y² when x = 7 and y = 6.
35. 35.If a − b = 2 and ab = 80, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 44².
37. 37.Use (a − b)² = a² − 2ab + b² to find 16².
38. 38.Use (a + b)(a − b) = a² − b² to find 81 × 79.
39. 39.Use (a − b)² = a² − 2ab + b² to find 39².
40. 40.Find the value of x² + 2xy + y² when x = 14 and y = 2.

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