Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 785 · 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 19².
2. 2.Use a² − b² = (a + b)(a − b) to find 55² − 47².
3. 3.Use (a + b)² = a² + 2ab + b² to find 105².
4. 4.Use (a + b)(a − b) = a² − b² to find 104 × 96.
5. 5.Use a² − b² = (a + b)(a − b) to find 53² − 19².
6. 6.Find the value of x² − 2xy + y² when x = 6 and y = 4.
7. 7.If a + b = 11 and ab = 24, what is a² + b²?
8. 8.Find the value of x² − 2xy + y² when x = 3 and y = 1.
9. 9.Use (a + b)(a − b) = a² − b² to find 51 × 49.
10. 10.Use (a − b)² = a² − 2ab + b² to find 53².
11. 11.Find the value of x² + 2xy + y² when x = 3 and y = 1.
12. 12.Use (a + b)² = a² + 2ab + b² to find 103².
13. 13.Use (a + b)² = a² + 2ab + b² to find 31².
14. 14.Find the value of x² − y² when x = 6 and y = 4.
15. 15.Use (a − b)² = a² − 2ab + b² to find 21².
16. 16.Use a² − b² = (a + b)(a − b) to find 31² − 26².
17. 17.Use (a + b)² = a² + 2ab + b² to find 13².
18. 18.If a + b = 10 and ab = 9, what is a² + b²?
19. 19.Find the value of x² − y² when x = 3 and y = 2.
20. 20.Find the value of x² − 2xy + y² when x = 5 and y = 4.
21. 21.Find the value of x² + 2xy + y² when x = 11 and y = 6.
22. 22.Use (a + b)(a − b) = a² − b² to find 55 × 45.
23. 23.Use (a + b)² = a² + 2ab + b² to find 27².
24. 24.If a + b = 15 and ab = 56, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 7 and y = 6.
26. 26.Use (a + b)² = a² + 2ab + b² to find 42².
27. 27.Use (a + b)² = a² + 2ab + b² to find 73².
28. 28.Use (a − b)² = a² − 2ab + b² to find 59².
29. 29.Use (a − b)² = a² − 2ab + b² to find 77².
30. 30.Find the value of x² + 2xy + y² when x = 8 and y = 7.
31. 31.Find the value of x² + 2xy + y² when x = 15 and y = 1.
32. 32.Find the value of x² + 2xy + y² when x = 5 and y = 4.
33. 33.Find the value of x² − 2xy + y² when x = 15 and y = 7.
34. 34.Find the value of x² + 2xy + y² when x = 5 and y = 3.
35. 35.Use (a − b)² = a² − 2ab + b² to find 11².
36. 36.Use a² − b² = (a + b)(a − b) to find 98² − 14².
37. 37.Find the value of x² − 2xy + y² when x = 12 and y = 11.
38. 38.Use (a + b)(a − b) = a² − b² to find 52 × 48.
39. 39.Use (a + b)² = a² + 2ab + b² to find 15².
40. 40.If a − b = 3 and ab = 88, what is a² + b²?

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