Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 47 · 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)(a − b) = a² − b² to find 75 × 65.
2. 2.Use (a + b)² = a² + 2ab + b² to find 59².
3. 3.Use (a + b)² = a² + 2ab + b² to find 49².
4. 4.Use (a + b)(a − b) = a² − b² to find 86 × 74.
5. 5.If a + b = 23 and ab = 132, what is a² + b²?
6. 6.If a + b = 11 and ab = 28, what is a² + b²?
7. 7.Use (a − b)² = a² − 2ab + b² to find 82².
8. 8.Use (a + b)(a − b) = a² − b² to find 62 × 58.
9. 9.Find the value of x² − 2xy + y² when x = 3 and y = 2.
10. 10.Use (a + b)(a − b) = a² − b² to find 32 × 28.
11. 11.If a − b = 8 and ab = 9, what is a² + b²?
12. 12.If a − b = 4 and ab = 5, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 61 × 59.
14. 14.If a − b = 1 and ab = 6, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 34² − 11².
16. 16.If a + b = 12 and ab = 35, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 39² − 8².
18. 18.Find the value of x² + 2xy + y² when x = 4 and y = 1.
19. 19.Use (a + b)² = a² + 2ab + b² to find 97².
20. 20.Use (a + b)(a − b) = a² − b² to find 63 × 57.
21. 21.Use (a + b)² = a² + 2ab + b² to find 81².
22. 22.Use (a + b)(a − b) = a² − b² to find 101 × 99.
23. 23.Use (a + b)(a − b) = a² − b² to find 25 × 15.
24. 24.Use (a + b)² = a² + 2ab + b² to find 68².
25. 25.Use a² − b² = (a + b)(a − b) to find 67² − 5².
26. 26.Find the value of x² − y² when x = 9 and y = 1.
27. 27.Use (a − b)² = a² − 2ab + b² to find 51².
28. 28.Use (a − b)² = a² − 2ab + b² to find 11².
29. 29.Use a² − b² = (a + b)(a − b) to find 32² − 20².
30. 30.Use (a + b)(a − b) = a² − b² to find 21 × 19.
31. 31.Use a² − b² = (a + b)(a − b) to find 60² − 29².
32. 32.If a + b = 3 and ab = 2, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 42² − 14².
34. 34.Use a² − b² = (a + b)(a − b) to find 33² − 28².
35. 35.Use (a + b)(a − b) = a² − b² to find 28 × 12.
36. 36.Find the value of x² − 2xy + y² when x = 11 and y = 8.
37. 37.Find the value of x² − y² when x = 11 and y = 3.
38. 38.Find the value of x² + 2xy + y² when x = 5 and y = 1.
39. 39.If a + b = 14 and ab = 24, what is a² + b²?
40. 40.Use (a + b)² = a² + 2ab + b² to find 17².

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