Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 590 · 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 51².
2. 2.Use (a − b)² = a² − 2ab + b² to find 25².
3. 3.Use (a + b)(a − b) = a² − b² to find 108 × 92.
4. 4.Use (a − b)² = a² − 2ab + b² to find 31².
5. 5.Use (a + b)(a − b) = a² − b² to find 72 × 68.
6. 6.Use (a + b)(a − b) = a² − b² to find 21 × 19.
7. 7.If a − b = 1 and ab = 6, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 73².
9. 9.Use (a + b)² = a² + 2ab + b² to find 15².
10. 10.If a − b = 2 and ab = 3, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 86².
12. 12.Use (a + b)² = a² + 2ab + b² to find 52².
13. 13.Use (a + b)(a − b) = a² − b² to find 23 × 17.
14. 14.Use (a − b)² = a² − 2ab + b² to find 38².
15. 15.Find the value of x² − y² when x = 12 and y = 3.
16. 16.Use (a + b)² = a² + 2ab + b² to find 87².
17. 17.If a + b = 10 and ab = 16, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 67².
19. 19.If a + b = 11 and ab = 30, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 102².
21. 21.Use (a + b)(a − b) = a² − b² to find 24 × 16.
22. 22.Use (a + b)(a − b) = a² − b² to find 36 × 24.
23. 23.Use a² − b² = (a + b)(a − b) to find 35² − 27².
24. 24.Use (a + b)(a − b) = a² − b² to find 92 × 88.
25. 25.Use (a + b)(a − b) = a² − b² to find 101 × 99.
26. 26.Use (a + b)² = a² + 2ab + b² to find 35².
27. 27.Use (a − b)² = a² − 2ab + b² to find 35².
28. 28.Use (a − b)² = a² − 2ab + b² to find 99².
29. 29.Find the value of x² − 2xy + y² when x = 5 and y = 4.
30. 30.Use (a + b)(a − b) = a² − b² to find 53 × 47.
31. 31.Use (a − b)² = a² − 2ab + b² to find 91².
32. 32.Use (a + b)² = a² + 2ab + b² to find 74².
33. 33.If a + b = 7 and ab = 12, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 96² − 77².
35. 35.If a + b = 19 and ab = 88, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 26² − 15².
37. 37.Use a² − b² = (a + b)(a − b) to find 25² − 14².
38. 38.If a + b = 9 and ab = 8, what is a² + b²?
39. 39.If a − b = 1 and ab = 20, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 27 × 13.

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