Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 43 · 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 42² − 1².
2. 2.Use (a + b)² = a² + 2ab + b² to find 109².
3. 3.Use (a − b)² = a² − 2ab + b² to find 24².
4. 4.Find the value of x² − 2xy + y² when x = 6 and y = 4.
5. 5.Use (a + b)(a − b) = a² − b² to find 21 × 19.
6. 6.Use (a + b)² = a² + 2ab + b² to find 17².
7. 7.Use a² − b² = (a + b)(a − b) to find 91² − 77².
8. 8.Find the value of x² − y² when x = 13 and y = 1.
9. 9.Use (a + b)² = a² + 2ab + b² to find 62².
10. 10.Use a² − b² = (a + b)(a − b) to find 73² − 5².
11. 11.Use (a + b)(a − b) = a² − b² to find 39 × 21.
12. 12.Use (a + b)(a − b) = a² − b² to find 101 × 99.
13. 13.Use (a − b)² = a² − 2ab + b² to find 12².
14. 14.Use a² − b² = (a + b)(a − b) to find 57² − 47².
15. 15.Find the value of x² + 2xy + y² when x = 7 and y = 2.
16. 16.Use a² − b² = (a + b)(a − b) to find 31² − 2².
17. 17.Use (a + b)(a − b) = a² − b² to find 33 × 27.
18. 18.Use a² − b² = (a + b)(a − b) to find 53² − 14².
19. 19.Use (a + b)(a − b) = a² − b² to find 34 × 26.
20. 20.Use (a − b)² = a² − 2ab + b² to find 43².
21. 21.Use (a − b)² = a² − 2ab + b² to find 75².
22. 22.If a + b = 9 and ab = 18, what is a² + b²?
23. 23.If a + b = 12 and ab = 27, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 66² − 17².
25. 25.If a + b = 14 and ab = 33, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 90² − 4².
27. 27.Use (a − b)² = a² − 2ab + b² to find 58².
28. 28.Use (a + b)² = a² + 2ab + b² to find 82².
29. 29.Use (a + b)² = a² + 2ab + b² to find 31².
30. 30.Use (a + b)² = a² + 2ab + b² to find 52².
31. 31.Use (a + b)² = a² + 2ab + b² to find 34².
32. 32.Find the value of x² + 2xy + y² when x = 9 and y = 2.
33. 33.Use (a + b)² = a² + 2ab + b² to find 93².
34. 34.Find the value of x² + 2xy + y² when x = 15 and y = 5.
35. 35.Use (a − b)² = a² − 2ab + b² to find 29².
36. 36.Use (a + b)² = a² + 2ab + b² to find 13².
37. 37.If a + b = 17 and ab = 70, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 54 × 46.
39. 39.If a + b = 3 and ab = 2, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 35².

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