Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 274 · 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 74².
2. 2.Use a² − b² = (a + b)(a − b) to find 53² − 49².
3. 3.Use (a + b)² = a² + 2ab + b² to find 103².
4. 4.Use (a + b)² = a² + 2ab + b² to find 82².
5. 5.Use a² − b² = (a + b)(a − b) to find 37² − 14².
6. 6.Use (a + b)(a − b) = a² − b² to find 88 × 72.
7. 7.Use (a + b)(a − b) = a² − b² to find 81 × 79.
8. 8.Use (a + b)(a − b) = a² − b² to find 91 × 89.
9. 9.If a + b = 3 and ab = 2, what is a² + b²?
10. 10.If a + b = 14 and ab = 45, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 84² − 16².
12. 12.Use (a + b)(a − b) = a² − b² to find 37 × 23.
13. 13.Find the value of x² + 2xy + y² when x = 13 and y = 3.
14. 14.Use a² − b² = (a + b)(a − b) to find 79² − 61².
15. 15.Find the value of x² − y² when x = 5 and y = 4.
16. 16.Use a² − b² = (a + b)(a − b) to find 26² − 24².
17. 17.Use (a − b)² = a² − 2ab + b² to find 49².
18. 18.Use (a − b)² = a² − 2ab + b² to find 81².
19. 19.Find the value of x² + 2xy + y² when x = 15 and y = 8.
20. 20.Find the value of x² + 2xy + y² when x = 3 and y = 2.
21. 21.Use (a + b)(a − b) = a² − b² to find 35 × 25.
22. 22.Find the value of x² + 2xy + y² when x = 10 and y = 2.
23. 23.If a − b = 5 and ab = 84, what is a² + b²?
24. 24.Use (a + b)² = a² + 2ab + b² to find 77².
25. 25.If a + b = 9 and ab = 20, what is a² + b²?
26. 26.Find the value of x² + 2xy + y² when x = 15 and y = 13.
27. 27.Use (a − b)² = a² − 2ab + b² to find 39².
28. 28.Use (a + b)(a − b) = a² − b² to find 39 × 21.
29. 29.Find the value of x² + 2xy + y² when x = 4 and y = 2.
30. 30.Find the value of x² − 2xy + y² when x = 9 and y = 5.
31. 31.If a − b = 2 and ab = 48, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 79².
33. 33.Use (a + b)² = a² + 2ab + b² to find 76².
34. 34.Use (a + b)² = a² + 2ab + b² to find 17².
35. 35.Find the value of x² − y² when x = 12 and y = 7.
36. 36.If a + b = 6 and ab = 8, what is a² + b²?
37. 37.Find the value of x² + 2xy + y² when x = 5 and y = 1.
38. 38.Use (a + b)² = a² + 2ab + b² to find 96².
39. 39.If a − b = 1 and ab = 6, what is a² + b²?
40. 40.Find the value of x² − 2xy + y² when x = 4 and y = 2.

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