Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 594 · 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 38².
2. 2.Use (a + b)² = a² + 2ab + b² to find 94².
3. 3.Use a² − b² = (a + b)(a − b) to find 23² − 6².
4. 4.Use (a + b)(a − b) = a² − b² to find 103 × 97.
5. 5.If a + b = 7 and ab = 12, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 66 × 54.
7. 7.Use (a + b)² = a² + 2ab + b² to find 61².
8. 8.Use a² − b² = (a + b)(a − b) to find 55² − 54².
9. 9.Use a² − b² = (a + b)(a − b) to find 28² − 6².
10. 10.Use a² − b² = (a + b)(a − b) to find 69² − 22².
11. 11.Use (a + b)(a − b) = a² − b² to find 48 × 32.
12. 12.Use (a + b)(a − b) = a² − b² to find 83 × 77.
13. 13.Use a² − b² = (a + b)(a − b) to find 71² − 24².
14. 14.Find the value of x² − 2xy + y² when x = 13 and y = 1.
15. 15.Use a² − b² = (a + b)(a − b) to find 77² − 17².
16. 16.Find the value of x² − y² when x = 10 and y = 9.
17. 17.Use (a + b)(a − b) = a² − b² to find 25 × 15.
18. 18.Use (a + b)² = a² + 2ab + b² to find 85².
19. 19.Use (a − b)² = a² − 2ab + b² to find 15².
20. 20.Use (a − b)² = a² − 2ab + b² to find 16².
21. 21.Find the value of x² + 2xy + y² when x = 5 and y = 1.
22. 22.If a + b = 5 and ab = 4, what is a² + b²?
23. 23.If a + b = 14 and ab = 48, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 68².
25. 25.If a − b = 3 and ab = 28, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 31².
27. 27.Use (a − b)² = a² − 2ab + b² to find 87².
28. 28.Find the value of x² + 2xy + y² when x = 7 and y = 1.
29. 29.Use a² − b² = (a + b)(a − b) to find 82² − 53².
30. 30.Use (a + b)(a − b) = a² − b² to find 73 × 67.
31. 31.Use (a + b)² = a² + 2ab + b² to find 29².
32. 32.Use (a − b)² = a² − 2ab + b² to find 48².
33. 33.Use (a − b)² = a² − 2ab + b² to find 96².
34. 34.If a + b = 6 and ab = 5, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 87² − 61².
36. 36.Use (a + b)² = a² + 2ab + b² to find 19².
37. 37.Use (a + b)² = a² + 2ab + b² to find 95².
38. 38.If a − b = 2 and ab = 3, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 72².
40. 40.Find the value of x² + 2xy + y² when x = 13 and y = 2.

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