Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 585 · 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 94² − 37².
2. 2.If a + b = 14 and ab = 48, what is a² + b²?
3. 3.Use (a − b)² = a² − 2ab + b² to find 47².
4. 4.Use (a − b)² = a² − 2ab + b² to find 87².
5. 5.Find the value of x² + 2xy + y² when x = 3 and y = 2.
6. 6.If a + b = 12 and ab = 35, what is a² + b²?
7. 7.If a − b = 6 and ab = 55, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 26² − 8².
9. 9.Find the value of x² + 2xy + y² when x = 5 and y = 1.
10. 10.Use (a − b)² = a² − 2ab + b² to find 45².
11. 11.If a + b = 20 and ab = 96, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 97² − 96².
13. 13.Use (a + b)(a − b) = a² − b² to find 74 × 66.
14. 14.Use (a − b)² = a² − 2ab + b² to find 95².
15. 15.Find the value of x² + 2xy + y² when x = 13 and y = 3.
16. 16.Use (a + b)² = a² + 2ab + b² to find 45².
17. 17.Use (a − b)² = a² − 2ab + b² to find 25².
18. 18.Find the value of x² + 2xy + y² when x = 14 and y = 11.
19. 19.Find the value of x² + 2xy + y² when x = 10 and y = 3.
20. 20.Find the value of x² + 2xy + y² when x = 15 and y = 1.
21. 21.If a − b = 11 and ab = 12, what is a² + b²?
22. 22.If a + b = 6 and ab = 8, what is a² + b²?
23. 23.If a + b = 11 and ab = 10, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 56².
25. 25.If a − b = 10 and ab = 24, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 71².
27. 27.Use a² − b² = (a + b)(a − b) to find 41² − 17².
28. 28.Use (a + b)² = a² + 2ab + b² to find 16².
29. 29.Use a² − b² = (a + b)(a − b) to find 36² − 18².
30. 30.Find the value of x² + 2xy + y² when x = 4 and y = 2.
31. 31.Use (a + b)² = a² + 2ab + b² to find 76².
32. 32.Use (a − b)² = a² − 2ab + b² to find 16².
33. 33.Use (a − b)² = a² − 2ab + b² to find 65².
34. 34.Use (a − b)² = a² − 2ab + b² to find 28².
35. 35.Find the value of x² − 2xy + y² when x = 10 and y = 6.
36. 36.Use (a + b)² = a² + 2ab + b² to find 26².
37. 37.Find the value of x² + 2xy + y² when x = 4 and y = 1.
38. 38.Use (a + b)(a − b) = a² − b² to find 106 × 94.
39. 39.Use a² − b² = (a + b)(a − b) to find 36² − 26².
40. 40.Use (a + b)² = a² + 2ab + b² to find 17².

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