Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 617 · 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 − y² when x = 4 and y = 3.
2. 2.Find the value of x² + 2xy + y² when x = 10 and y = 7.
3. 3.Find the value of x² − y² when x = 8 and y = 4.
4. 4.Use (a + b)² = a² + 2ab + b² to find 93².
5. 5.Use (a − b)² = a² − 2ab + b² to find 97².
6. 6.If a + b = 5 and ab = 6, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 26².
8. 8.Find the value of x² + 2xy + y² when x = 13 and y = 7.
9. 9.Use (a + b)² = a² + 2ab + b² to find 19².
10. 10.Find the value of x² − y² when x = 15 and y = 1.
11. 11.Use (a − b)² = a² − 2ab + b² to find 58².
12. 12.Find the value of x² + 2xy + y² when x = 4 and y = 2.
13. 13.Use (a − b)² = a² − 2ab + b² to find 27².
14. 14.Use (a − b)² = a² − 2ab + b² to find 68².
15. 15.If a + b = 10 and ab = 24, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 27² − 16².
17. 17.Find the value of x² − 2xy + y² when x = 9 and y = 6.
18. 18.Find the value of x² + 2xy + y² when x = 14 and y = 1.
19. 19.Use a² − b² = (a + b)(a − b) to find 47² − 15².
20. 20.Use (a + b)(a − b) = a² − b² to find 105 × 95.
21. 21.Use (a − b)² = a² − 2ab + b² to find 35².
22. 22.Use (a + b)(a − b) = a² − b² to find 64 × 56.
23. 23.Use (a + b)² = a² + 2ab + b² to find 59².
24. 24.Use (a − b)² = a² − 2ab + b² to find 81².
25. 25.Use (a + b)(a − b) = a² − b² to find 92 × 88.
26. 26.Use (a + b)² = a² + 2ab + b² to find 38².
27. 27.Use (a + b)² = a² + 2ab + b² to find 72².
28. 28.Use (a + b)(a − b) = a² − b² to find 93 × 87.
29. 29.If a − b = 8 and ab = 9, what is a² + b²?
30. 30.Find the value of x² − y² when x = 13 and y = 7.
31. 31.Use (a + b)² = a² + 2ab + b² to find 92².
32. 32.Use (a + b)² = a² + 2ab + b² to find 32².
33. 33.Use (a + b)(a − b) = a² − b² to find 43 × 37.
34. 34.Use (a + b)(a − b) = a² − b² to find 37 × 23.
35. 35.Find the value of x² − 2xy + y² when x = 13 and y = 6.
36. 36.Use (a − b)² = a² − 2ab + b² to find 39².
37. 37.Use a² − b² = (a + b)(a − b) to find 33² − 14².
38. 38.Use (a + b)(a − b) = a² − b² to find 39 × 21.
39. 39.Use (a + b)(a − b) = a² − b² to find 72 × 68.
40. 40.Use (a − b)² = a² − 2ab + b² to find 31².

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