Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 130 · 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.If a − b = 2 and ab = 3, what is a² + b²?
2. 2.Find the value of x² + 2xy + y² when x = 4 and y = 3.
3. 3.Use (a + b)² = a² + 2ab + b² to find 35².
4. 4.If a + b = 8 and ab = 15, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 104².
6. 6.Use (a − b)² = a² − 2ab + b² to find 85².
7. 7.Find the value of x² − y² when x = 15 and y = 7.
8. 8.Use (a + b)(a − b) = a² − b² to find 27 × 13.
9. 9.Use a² − b² = (a + b)(a − b) to find 36² − 7².
10. 10.Use (a − b)² = a² − 2ab + b² to find 22².
11. 11.Use (a + b)² = a² + 2ab + b² to find 29².
12. 12.If a + b = 7 and ab = 12, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 51².
14. 14.Use (a + b)² = a² + 2ab + b² to find 26².
15. 15.Use (a + b)(a − b) = a² − b² to find 38 × 22.
16. 16.If a − b = 5 and ab = 50, what is a² + b²?
17. 17.Find the value of x² − y² when x = 12 and y = 9.
18. 18.Use (a + b)² = a² + 2ab + b² to find 58².
19. 19.If a + b = 15 and ab = 56, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 79².
21. 21.Find the value of x² − 2xy + y² when x = 13 and y = 6.
22. 22.Find the value of x² − 2xy + y² when x = 15 and y = 14.
23. 23.Use a² − b² = (a + b)(a − b) to find 63² − 47².
24. 24.Use a² − b² = (a + b)(a − b) to find 96² − 57².
25. 25.Use (a − b)² = a² − 2ab + b² to find 19².
26. 26.Use (a − b)² = a² − 2ab + b² to find 54².
27. 27.Use (a + b)² = a² + 2ab + b² to find 24².
28. 28.Use (a − b)² = a² − 2ab + b² to find 33².
29. 29.Use (a + b)(a − b) = a² − b² to find 54 × 46.
30. 30.Use a² − b² = (a + b)(a − b) to find 55² − 16².
31. 31.Use (a + b)(a − b) = a² − b² to find 75 × 65.
32. 32.Use (a − b)² = a² − 2ab + b² to find 47².
33. 33.Use (a + b)(a − b) = a² − b² to find 103 × 97.
34. 34.Use (a − b)² = a² − 2ab + b² to find 73².
35. 35.Use (a + b)² = a² + 2ab + b² to find 11².
36. 36.Use (a + b)² = a² + 2ab + b² to find 59².
37. 37.Use (a + b)(a − b) = a² − b² to find 72 × 68.
38. 38.Use (a + b)(a − b) = a² − b² to find 65 × 55.
39. 39.Use (a − b)² = a² − 2ab + b² to find 55².
40. 40.If a − b = 3 and ab = 40, what is a² + b²?

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