Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 106 · 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 58² − 27².
2. 2.Use (a − b)² = a² − 2ab + b² to find 62².
3. 3.Use (a − b)² = a² − 2ab + b² to find 19².
4. 4.If a + b = 6 and ab = 8, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 39².
6. 6.Find the value of x² − 2xy + y² when x = 7 and y = 2.
7. 7.Use (a + b)(a − b) = a² − b² to find 31 × 29.
8. 8.Use (a + b)(a − b) = a² − b² to find 72 × 68.
9. 9.Use (a + b)² = a² + 2ab + b² to find 15².
10. 10.Use (a + b)² = a² + 2ab + b² to find 32².
11. 11.Use a² − b² = (a + b)(a − b) to find 43² − 6².
12. 12.Find the value of x² + 2xy + y² when x = 7 and y = 1.
13. 13.Use a² − b² = (a + b)(a − b) to find 45² − 5².
14. 14.Use a² − b² = (a + b)(a − b) to find 40² − 32².
15. 15.Use a² − b² = (a + b)(a − b) to find 46² − 30².
16. 16.Use (a − b)² = a² − 2ab + b² to find 49².
17. 17.Find the value of x² + 2xy + y² when x = 12 and y = 2.
18. 18.If a + b = 12 and ab = 35, what is a² + b²?
19. 19.If a + b = 16 and ab = 48, what is a² + b²?
20. 20.If a + b = 7 and ab = 12, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 89².
22. 22.Use (a + b)² = a² + 2ab + b² to find 66².
23. 23.Use (a + b)² = a² + 2ab + b² to find 64².
24. 24.Use (a − b)² = a² − 2ab + b² to find 38².
25. 25.Use (a + b)(a − b) = a² − b² to find 53 × 47.
26. 26.Use (a − b)² = a² − 2ab + b² to find 76².
27. 27.Use (a + b)² = a² + 2ab + b² to find 19².
28. 28.Use (a − b)² = a² − 2ab + b² to find 93².
29. 29.Use a² − b² = (a + b)(a − b) to find 88² − 60².
30. 30.Find the value of x² − y² when x = 3 and y = 1.
31. 31.Use (a − b)² = a² − 2ab + b² to find 32².
32. 32.Find the value of x² − y² when x = 11 and y = 9.
33. 33.Use (a − b)² = a² − 2ab + b² to find 91².
34. 34.Use (a + b)(a − b) = a² − b² to find 67 × 53.
35. 35.If a + b = 10 and ab = 9, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 56².
37. 37.If a − b = 6 and ab = 16, what is a² + b²?
38. 38.Find the value of x² − 2xy + y² when x = 9 and y = 1.
39. 39.Find the value of x² − 2xy + y² when x = 10 and y = 1.
40. 40.Use a² − b² = (a + b)(a − b) to find 27² − 18².

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