Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 382 · 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 63².
2. 2.Find the value of x² − y² when x = 5 and y = 2.
3. 3.Find the value of x² + 2xy + y² when x = 4 and y = 1.
4. 4.Find the value of x² − y² when x = 6 and y = 1.
5. 5.If a + b = 18 and ab = 80, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 96².
7. 7.Use a² − b² = (a + b)(a − b) to find 56² − 10².
8. 8.Use (a + b)² = a² + 2ab + b² to find 13².
9. 9.Use (a + b)² = a² + 2ab + b² to find 104².
10. 10.Use a² − b² = (a + b)(a − b) to find 45² − 24².
11. 11.Use (a − b)² = a² − 2ab + b² to find 84².
12. 12.Use (a + b)(a − b) = a² − b² to find 74 × 66.
13. 13.Use (a + b)(a − b) = a² − b² to find 46 × 34.
14. 14.Find the value of x² − 2xy + y² when x = 6 and y = 1.
15. 15.Use (a + b)² = a² + 2ab + b² to find 29².
16. 16.If a − b = 5 and ab = 14, what is a² + b²?
17. 17.Find the value of x² − 2xy + y² when x = 12 and y = 5.
18. 18.Use (a + b)(a − b) = a² − b² to find 52 × 48.
19. 19.If a + b = 4 and ab = 3, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 57² − 2².
21. 21.Use (a + b)² = a² + 2ab + b² to find 14².
22. 22.If a + b = 3 and ab = 2, what is a² + b²?
23. 23.If a + b = 14 and ab = 45, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 99 × 81.
25. 25.Use (a + b)(a − b) = a² − b² to find 55 × 45.
26. 26.Use (a + b)(a − b) = a² − b² to find 42 × 38.
27. 27.Use a² − b² = (a + b)(a − b) to find 91² − 61².
28. 28.Use (a + b)² = a² + 2ab + b² to find 83².
29. 29.Find the value of x² + 2xy + y² when x = 4 and y = 3.
30. 30.If a − b = 6 and ab = 27, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 44².
32. 32.Use a² − b² = (a + b)(a − b) to find 95² − 56².
33. 33.If a + b = 13 and ab = 40, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 39².
35. 35.Use (a − b)² = a² − 2ab + b² to find 47².
36. 36.If a + b = 11 and ab = 30, what is a² + b²?
37. 37.If a + b = 5 and ab = 4, what is a² + b²?
38. 38.Use (a + b)(a − b) = a² − b² to find 101 × 99.
39. 39.Use a² − b² = (a + b)(a − b) to find 61² − 20².
40. 40.If a + b = 13 and ab = 30, what is a² + b²?

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