Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 73 · 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.Find the value of x² − y² when x = 3 and y = 1.
2. 2.Use a² − b² = (a + b)(a − b) to find 22² − 5².
3. 3.Use (a + b)(a − b) = a² − b² to find 72 × 68.
4. 4.Use a² − b² = (a + b)(a − b) to find 72² − 47².
5. 5.Use (a − b)² = a² − 2ab + b² to find 89².
6. 6.If a + b = 5 and ab = 6, what is a² + b²?
7. 7.Use (a + b)(a − b) = a² − b² to find 33 × 27.
8. 8.Use (a + b)² = a² + 2ab + b² to find 66².
9. 9.Use (a + b)² = a² + 2ab + b² to find 15².
10. 10.If a + b = 5 and ab = 4, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 58².
12. 12.If a + b = 3 and ab = 2, what is a² + b²?
13. 13.Use a² − b² = (a + b)(a − b) to find 82² − 24².
14. 14.Use (a + b)² = a² + 2ab + b² to find 87².
15. 15.Find the value of x² − y² when x = 4 and y = 2.
16. 16.Use (a + b)(a − b) = a² − b² to find 105 × 95.
17. 17.Use (a + b)² = a² + 2ab + b² to find 46².
18. 18.Use (a + b)² = a² + 2ab + b² to find 91².
19. 19.If a − b = 9 and ab = 36, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 30² − 2².
21. 21.Use (a − b)² = a² − 2ab + b² to find 19².
22. 22.Use (a + b)² = a² + 2ab + b² to find 43².
23. 23.Use (a − b)² = a² − 2ab + b² to find 74².
24. 24.If a − b = 2 and ab = 35, what is a² + b²?
25. 25.If a − b = 1 and ab = 2, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 85² − 65².
27. 27.If a − b = 3 and ab = 28, what is a² + b²?
28. 28.Find the value of x² + 2xy + y² when x = 4 and y = 3.
29. 29.Use (a + b)² = a² + 2ab + b² to find 77².
30. 30.Use (a + b)² = a² + 2ab + b² to find 61².
31. 31.Use (a + b)(a − b) = a² − b² to find 31 × 29.
32. 32.Use (a + b)(a − b) = a² − b² to find 71 × 69.
33. 33.Find the value of x² + 2xy + y² when x = 4 and y = 1.
34. 34.If a − b = 1 and ab = 56, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 35².
36. 36.Find the value of x² − 2xy + y² when x = 5 and y = 1.
37. 37.Use (a + b)(a − b) = a² − b² to find 52 × 48.
38. 38.Find the value of x² − 2xy + y² when x = 14 and y = 8.
39. 39.Use a² − b² = (a + b)(a − b) to find 73² − 6².
40. 40.Find the value of x² − y² when x = 8 and y = 6.

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