Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 107 · 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 49².
2. 2.Use a² − b² = (a + b)(a − b) to find 38² − 9².
3. 3.Use a² − b² = (a + b)(a − b) to find 69² − 17².
4. 4.Use a² − b² = (a + b)(a − b) to find 57² − 36².
5. 5.Find the value of x² + 2xy + y² when x = 15 and y = 12.
6. 6.Find the value of x² − 2xy + y² when x = 9 and y = 8.
7. 7.Use (a − b)² = a² − 2ab + b² to find 69².
8. 8.Use (a + b)² = a² + 2ab + b² to find 13².
9. 9.Use (a − b)² = a² − 2ab + b² to find 39².
10. 10.Use a² − b² = (a + b)(a − b) to find 22² − 5².
11. 11.Use (a − b)² = a² − 2ab + b² to find 77².
12. 12.Use (a + b)(a − b) = a² − b² to find 101 × 99.
13. 13.Use (a − b)² = a² − 2ab + b² to find 54².
14. 14.Use a² − b² = (a + b)(a − b) to find 34² − 27².
15. 15.Use (a + b)² = a² + 2ab + b² to find 103².
16. 16.If a + b = 15 and ab = 36, what is a² + b²?
17. 17.If a − b = 5 and ab = 84, what is a² + b²?
18. 18.If a − b = 4 and ab = 5, what is a² + b²?
19. 19.If a + b = 9 and ab = 20, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 76².
21. 21.Find the value of x² − y² when x = 7 and y = 4.
22. 22.Use (a + b)(a − b) = a² − b² to find 108 × 92.
23. 23.Use (a − b)² = a² − 2ab + b² to find 53².
24. 24.If a + b = 3 and ab = 2, what is a² + b²?
25. 25.Use (a + b)(a − b) = a² − b² to find 22 × 18.
26. 26.Find the value of x² − 2xy + y² when x = 14 and y = 3.
27. 27.Use (a + b)² = a² + 2ab + b² to find 99².
28. 28.Use a² − b² = (a + b)(a − b) to find 69² − 21².
29. 29.Find the value of x² + 2xy + y² when x = 9 and y = 2.
30. 30.Find the value of x² − y² when x = 6 and y = 3.
31. 31.Use (a − b)² = a² − 2ab + b² to find 19².
32. 32.If a − b = 4 and ab = 12, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 12 and y = 1.
34. 34.If a + b = 5 and ab = 6, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 14².
36. 36.Find the value of x² + 2xy + y² when x = 13 and y = 8.
37. 37.Find the value of x² + 2xy + y² when x = 5 and y = 1.
38. 38.Use a² − b² = (a + b)(a − b) to find 26² − 24².
39. 39.If a − b = 3 and ab = 54, what is a² + b²?
40. 40.If a − b = 6 and ab = 55, what is a² + b²?

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