Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 846 · 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.Find the value of x² − 2xy + y² when x = 7 and y = 5.
2. 2.Use (a + b)(a − b) = a² − b² to find 73 × 67.
3. 3.Use a² − b² = (a + b)(a − b) to find 64² − 23².
4. 4.Find the value of x² + 2xy + y² when x = 13 and y = 4.
5. 5.If a − b = 7 and ab = 8, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 52² − 27².
7. 7.Use (a − b)² = a² − 2ab + b² to find 73².
8. 8.Use (a + b)(a − b) = a² − b² to find 43 × 37.
9. 9.Use (a + b)(a − b) = a² − b² to find 35 × 25.
10. 10.Find the value of x² − 2xy + y² when x = 3 and y = 2.
11. 11.If a + b = 5 and ab = 6, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 24 × 16.
13. 13.If a − b = 9 and ab = 36, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 61².
15. 15.Use a² − b² = (a + b)(a − b) to find 82² − 80².
16. 16.Use (a + b)² = a² + 2ab + b² to find 94².
17. 17.Use (a + b)(a − b) = a² − b² to find 88 × 72.
18. 18.Use (a + b)² = a² + 2ab + b² to find 89².
19. 19.Find the value of x² − y² when x = 7 and y = 2.
20. 20.Find the value of x² − 2xy + y² when x = 7 and y = 2.
21. 21.Use (a + b)² = a² + 2ab + b² to find 66².
22. 22.Use (a − b)² = a² − 2ab + b² to find 62².
23. 23.Use (a − b)² = a² − 2ab + b² to find 71².
24. 24.Use (a + b)² = a² + 2ab + b² to find 15².
25. 25.Use (a − b)² = a² − 2ab + b² to find 59².
26. 26.If a − b = 6 and ab = 40, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 36 × 24.
28. 28.If a + b = 4 and ab = 3, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 104².
30. 30.Use (a − b)² = a² − 2ab + b² to find 72².
31. 31.Use (a + b)² = a² + 2ab + b² to find 58².
32. 32.Use (a + b)² = a² + 2ab + b² to find 36².
33. 33.Use a² − b² = (a + b)(a − b) to find 63² − 13².
34. 34.Find the value of x² + 2xy + y² when x = 4 and y = 1.
35. 35.Use (a − b)² = a² − 2ab + b² to find 28².
36. 36.Use a² − b² = (a + b)(a − b) to find 55² − 34².
37. 37.Use (a + b)² = a² + 2ab + b² to find 12².
38. 38.Find the value of x² − y² when x = 6 and y = 4.
39. 39.If a − b = 4 and ab = 21, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 56² − 50².

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