Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 68 · 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 47².
2. 2.Use (a + b)² = a² + 2ab + b² to find 14².
3. 3.Use (a + b)² = a² + 2ab + b² to find 62².
4. 4.Use (a − b)² = a² − 2ab + b² to find 97².
5. 5.Use a² − b² = (a + b)(a − b) to find 24² − 21².
6. 6.Use (a + b)² = a² + 2ab + b² to find 65².
7. 7.Find the value of x² − 2xy + y² when x = 3 and y = 2.
8. 8.Find the value of x² + 2xy + y² when x = 9 and y = 7.
9. 9.If a − b = 2 and ab = 24, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 27².
11. 11.Use (a + b)(a − b) = a² − b² to find 78 × 62.
12. 12.Use (a + b)² = a² + 2ab + b² to find 91².
13. 13.Use (a + b)² = a² + 2ab + b² to find 108².
14. 14.Use (a + b)² = a² + 2ab + b² to find 31².
15. 15.If a − b = 2 and ab = 3, what is a² + b²?
16. 16.Find the value of x² − 2xy + y² when x = 9 and y = 8.
17. 17.If a + b = 5 and ab = 4, what is a² + b²?
18. 18.Find the value of x² − 2xy + y² when x = 8 and y = 6.
19. 19.Use (a + b)(a − b) = a² − b² to find 45 × 35.
20. 20.Find the value of x² + 2xy + y² when x = 4 and y = 3.
21. 21.Use (a + b)² = a² + 2ab + b² to find 57².
22. 22.If a − b = 5 and ab = 6, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 45².
24. 24.Use (a − b)² = a² − 2ab + b² to find 89².
25. 25.If a − b = 4 and ab = 5, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 53 × 47.
27. 27.Use (a + b)² = a² + 2ab + b² to find 68².
28. 28.Use (a − b)² = a² − 2ab + b² to find 44².
29. 29.Use (a − b)² = a² − 2ab + b² to find 23².
30. 30.Find the value of x² − 2xy + y² when x = 5 and y = 2.
31. 31.Use a² − b² = (a + b)(a − b) to find 34² − 22².
32. 32.Use (a − b)² = a² − 2ab + b² to find 38².
33. 33.Use (a + b)(a − b) = a² − b² to find 81 × 79.
34. 34.Use a² − b² = (a + b)(a − b) to find 23² − 9².
35. 35.Use (a + b)(a − b) = a² − b² to find 98 × 82.
36. 36.If a + b = 3 and ab = 2, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 43².
38. 38.Use a² − b² = (a + b)(a − b) to find 85² − 60².
39. 39.Find the value of x² − y² when x = 3 and y = 2.
40. 40.Use (a − b)² = a² − 2ab + b² to find 48².

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