Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 709 · 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 84².
2. 2.Use a² − b² = (a + b)(a − b) to find 68² − 53².
3. 3.Use a² − b² = (a + b)(a − b) to find 56² − 12².
4. 4.Use a² − b² = (a + b)(a − b) to find 64² − 1².
5. 5.Use (a + b)² = a² + 2ab + b² to find 68².
6. 6.Use (a + b)² = a² + 2ab + b² to find 86².
7. 7.Use (a + b)² = a² + 2ab + b² to find 13².
8. 8.Use a² − b² = (a + b)(a − b) to find 40² − 35².
9. 9.Use (a + b)(a − b) = a² − b² to find 32 × 28.
10. 10.Use (a + b)² = a² + 2ab + b² to find 103².
11. 11.Use (a + b)² = a² + 2ab + b² to find 46².
12. 12.Use a² − b² = (a + b)(a − b) to find 72² − 9².
13. 13.Use (a + b)² = a² + 2ab + b² to find 41².
14. 14.If a − b = 6 and ab = 55, what is a² + b²?
15. 15.Use (a − b)² = a² − 2ab + b² to find 29².
16. 16.If a + b = 6 and ab = 8, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 31².
18. 18.Find the value of x² + 2xy + y² when x = 7 and y = 1.
19. 19.Use (a + b)(a − b) = a² − b² to find 69 × 51.
20. 20.Use a² − b² = (a + b)(a − b) to find 59² − 19².
21. 21.Find the value of x² − 2xy + y² when x = 11 and y = 8.
22. 22.Use (a − b)² = a² − 2ab + b² to find 61².
23. 23.Use (a + b)(a − b) = a² − b² to find 28 × 12.
24. 24.If a + b = 6 and ab = 5, what is a² + b²?
25. 25.Find the value of x² − y² when x = 12 and y = 8.
26. 26.Find the value of x² − y² when x = 9 and y = 5.
27. 27.If a − b = 4 and ab = 5, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 65².
29. 29.Use a² − b² = (a + b)(a − b) to find 64² − 12².
30. 30.Use (a − b)² = a² − 2ab + b² to find 96².
31. 31.If a + b = 3 and ab = 2, what is a² + b²?
32. 32.Find the value of x² + 2xy + y² when x = 7 and y = 6.
33. 33.Find the value of x² + 2xy + y² when x = 4 and y = 2.
34. 34.Use (a − b)² = a² − 2ab + b² to find 66².
35. 35.Use a² − b² = (a + b)(a − b) to find 47² − 45².
36. 36.If a − b = 5 and ab = 6, what is a² + b²?
37. 37.Use a² − b² = (a + b)(a − b) to find 65² − 28².
38. 38.Use a² − b² = (a + b)(a − b) to find 67² − 53².
39. 39.Use (a + b)² = a² + 2ab + b² to find 82².
40. 40.If a + b = 11 and ab = 30, what is a² + b²?

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