Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 607 · 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 a² − b² = (a + b)(a − b) to find 86² − 16².
2. 2.Use a² − b² = (a + b)(a − b) to find 27² − 23².
3. 3.Use (a − b)² = a² − 2ab + b² to find 45².
4. 4.Use (a + b)² = a² + 2ab + b² to find 21².
5. 5.Use (a + b)² = a² + 2ab + b² to find 28².
6. 6.Use (a − b)² = a² − 2ab + b² to find 13².
7. 7.Find the value of x² − 2xy + y² when x = 15 and y = 7.
8. 8.Use a² − b² = (a + b)(a − b) to find 79² − 41².
9. 9.If a − b = 5 and ab = 50, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 70² − 5².
11. 11.Use (a − b)² = a² − 2ab + b² to find 47².
12. 12.Find the value of x² + 2xy + y² when x = 12 and y = 10.
13. 13.Use a² − b² = (a + b)(a − b) to find 95² − 78².
14. 14.Use a² − b² = (a + b)(a − b) to find 35² − 4².
15. 15.Use a² − b² = (a + b)(a − b) to find 58² − 29².
16. 16.Use (a − b)² = a² − 2ab + b² to find 61².
17. 17.Find the value of x² − 2xy + y² when x = 8 and y = 1.
18. 18.Use (a + b)² = a² + 2ab + b² to find 41².
19. 19.Find the value of x² − 2xy + y² when x = 11 and y = 10.
20. 20.If a + b = 12 and ab = 32, what is a² + b²?
21. 21.Use (a + b)² = a² + 2ab + b² to find 27².
22. 22.Use (a + b)² = a² + 2ab + b² to find 78².
23. 23.Use a² − b² = (a + b)(a − b) to find 94² − 5².
24. 24.Use (a + b)² = a² + 2ab + b² to find 52².
25. 25.Use (a + b)² = a² + 2ab + b² to find 29².
26. 26.Use (a + b)(a − b) = a² − b² to find 37 × 23.
27. 27.Use (a + b)² = a² + 2ab + b² to find 36².
28. 28.Use a² − b² = (a + b)(a − b) to find 64² − 9².
29. 29.Find the value of x² − y² when x = 11 and y = 3.
30. 30.Use (a + b)(a − b) = a² − b² to find 54 × 46.
31. 31.If a + b = 5 and ab = 6, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 97².
33. 33.Use (a − b)² = a² − 2ab + b² to find 68².
34. 34.Use (a + b)(a − b) = a² − b² to find 58 × 42.
35. 35.If a + b = 16 and ab = 60, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 77².
37. 37.Find the value of x² − y² when x = 10 and y = 1.
38. 38.If a + b = 12 and ab = 11, what is a² + b²?
39. 39.Find the value of x² + 2xy + y² when x = 3 and y = 2.
40. 40.Find the value of x² + 2xy + y² when x = 13 and y = 8.

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