Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 375 · 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 27².
2. 2.Use (a + b)(a − b) = a² − b² to find 64 × 56.
3. 3.Find the value of x² − y² when x = 7 and y = 2.
4. 4.Use a² − b² = (a + b)(a − b) to find 76² − 52².
5. 5.Find the value of x² + 2xy + y² when x = 12 and y = 6.
6. 6.Use (a + b)² = a² + 2ab + b² to find 23².
7. 7.Find the value of x² + 2xy + y² when x = 10 and y = 5.
8. 8.Use a² − b² = (a + b)(a − b) to find 53² − 29².
9. 9.If a + b = 21 and ab = 108, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 69².
11. 11.Use (a − b)² = a² − 2ab + b² to find 45².
12. 12.If a − b = 2 and ab = 15, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 37².
14. 14.Use (a + b)² = a² + 2ab + b² to find 42².
15. 15.If a − b = 3 and ab = 4, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 14².
17. 17.Use (a + b)² = a² + 2ab + b² to find 47².
18. 18.Use (a + b)² = a² + 2ab + b² to find 94².
19. 19.Use (a + b)² = a² + 2ab + b² to find 82².
20. 20.Find the value of x² − y² when x = 11 and y = 10.
21. 21.Use (a − b)² = a² − 2ab + b² to find 82².
22. 22.Use (a − b)² = a² − 2ab + b² to find 11².
23. 23.Use (a + b)² = a² + 2ab + b² to find 17².
24. 24.Find the value of x² − y² when x = 15 and y = 3.
25. 25.Use (a − b)² = a² − 2ab + b² to find 15².
26. 26.Use (a + b)(a − b) = a² − b² to find 46 × 34.
27. 27.Find the value of x² + 2xy + y² when x = 6 and y = 3.
28. 28.If a − b = 7 and ab = 8, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 29².
30. 30.Use (a − b)² = a² − 2ab + b² to find 78².
31. 31.Use (a + b)(a − b) = a² − b² to find 55 × 45.
32. 32.Use (a − b)² = a² − 2ab + b² to find 33².
33. 33.If a − b = 3 and ab = 10, what is a² + b²?
34. 34.If a + b = 15 and ab = 54, what is a² + b²?
35. 35.If a + b = 4 and ab = 3, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 75².
37. 37.If a − b = 1 and ab = 132, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 103².
39. 39.Use (a − b)² = a² − 2ab + b² to find 75².
40. 40.If a + b = 11 and ab = 10, what is a² + b²?

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