Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 512 · 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.If a + b = 7 and ab = 6, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 37².
3. 3.Use (a − b)² = a² − 2ab + b² to find 46².
4. 4.Find the value of x² + 2xy + y² when x = 12 and y = 7.
5. 5.Use (a − b)² = a² − 2ab + b² to find 17².
6. 6.Find the value of x² + 2xy + y² when x = 4 and y = 3.
7. 7.Find the value of x² − y² when x = 10 and y = 2.
8. 8.Use (a + b)(a − b) = a² − b² to find 21 × 19.
9. 9.Use a² − b² = (a + b)(a − b) to find 56² − 12².
10. 10.Use a² − b² = (a + b)(a − b) to find 22² − 10².
11. 11.Use (a − b)² = a² − 2ab + b² to find 48².
12. 12.Find the value of x² − 2xy + y² when x = 4 and y = 2.
13. 13.If a + b = 23 and ab = 132, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 18².
15. 15.Use (a + b)(a − b) = a² − b² to find 73 × 67.
16. 16.Use a² − b² = (a + b)(a − b) to find 51² − 5².
17. 17.Use (a + b)(a − b) = a² − b² to find 67 × 53.
18. 18.Use (a + b)(a − b) = a² − b² to find 71 × 69.
19. 19.Use a² − b² = (a + b)(a − b) to find 96² − 50².
20. 20.Find the value of x² − 2xy + y² when x = 5 and y = 2.
21. 21.Use (a − b)² = a² − 2ab + b² to find 84².
22. 22.Use a² − b² = (a + b)(a − b) to find 44² − 10².
23. 23.Use (a − b)² = a² − 2ab + b² to find 79².
24. 24.Use (a + b)(a − b) = a² − b² to find 85 × 75.
25. 25.Use (a + b)² = a² + 2ab + b² to find 81².
26. 26.Use a² − b² = (a + b)(a − b) to find 54² − 29².
27. 27.Use (a + b)² = a² + 2ab + b² to find 96².
28. 28.If a − b = 2 and ab = 24, what is a² + b²?
29. 29.If a + b = 15 and ab = 56, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 78².
31. 31.Use a² − b² = (a + b)(a − b) to find 53² − 16².
32. 32.Use (a + b)(a − b) = a² − b² to find 31 × 29.
33. 33.Use a² − b² = (a + b)(a − b) to find 35² − 8².
34. 34.If a + b = 9 and ab = 18, what is a² + b²?
35. 35.Find the value of x² − y² when x = 13 and y = 3.
36. 36.Use a² − b² = (a + b)(a − b) to find 47² − 11².
37. 37.Use a² − b² = (a + b)(a − b) to find 47² − 1².
38. 38.Use (a + b)(a − b) = a² − b² to find 42 × 38.
39. 39.Find the value of x² − 2xy + y² when x = 6 and y = 2.
40. 40.Use (a + b)(a − b) = a² − b² to find 48 × 32.

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