Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 285 · 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 = 6 and y = 3.
2. 2.Use a² − b² = (a + b)(a − b) to find 20² − 10².
3. 3.Use (a + b)(a − b) = a² − b² to find 72 × 68.
4. 4.Use (a + b)² = a² + 2ab + b² to find 22².
5. 5.Use (a − b)² = a² − 2ab + b² to find 48².
6. 6.Use a² − b² = (a + b)(a − b) to find 99² − 74².
7. 7.If a + b = 5 and ab = 6, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 33 × 27.
9. 9.Use (a + b)(a − b) = a² − b² to find 95 × 85.
10. 10.Use (a + b)² = a² + 2ab + b² to find 102².
11. 11.Find the value of x² − y² when x = 9 and y = 1.
12. 12.If a + b = 12 and ab = 27, what is a² + b²?
13. 13.Use (a + b)(a − b) = a² − b² to find 48 × 32.
14. 14.Find the value of x² − y² when x = 9 and y = 5.
15. 15.Use (a + b)² = a² + 2ab + b² to find 88².
16. 16.If a − b = 2 and ab = 3, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 29².
18. 18.Use (a − b)² = a² − 2ab + b² to find 54².
19. 19.Use a² − b² = (a + b)(a − b) to find 96² − 14².
20. 20.Find the value of x² − y² when x = 7 and y = 5.
21. 21.Use (a − b)² = a² − 2ab + b² to find 88².
22. 22.If a − b = 6 and ab = 27, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 55² − 34².
24. 24.Find the value of x² + 2xy + y² when x = 7 and y = 4.
25. 25.Use (a − b)² = a² − 2ab + b² to find 31².
26. 26.Use (a − b)² = a² − 2ab + b² to find 66².
27. 27.Use (a + b)(a − b) = a² − b² to find 89 × 71.
28. 28.If a + b = 5 and ab = 4, what is a² + b²?
29. 29.Use (a − b)² = a² − 2ab + b² to find 79².
30. 30.If a + b = 9 and ab = 18, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 35² − 24².
32. 32.Use (a + b)² = a² + 2ab + b² to find 54².
33. 33.If a − b = 4 and ab = 60, what is a² + b²?
34. 34.Use a² − b² = (a + b)(a − b) to find 40² − 37².
35. 35.Find the value of x² − y² when x = 8 and y = 5.
36. 36.Use a² − b² = (a + b)(a − b) to find 81² − 17².
37. 37.Use a² − b² = (a + b)(a − b) to find 37² − 25².
38. 38.Use (a + b)(a − b) = a² − b² to find 31 × 29.
39. 39.Find the value of x² − 2xy + y² when x = 10 and y = 3.
40. 40.Find the value of x² − 2xy + y² when x = 3 and y = 2.

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