Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 317 · 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 − 2xy + y² when x = 12 and y = 8.
2. 2.Use (a + b)² = a² + 2ab + b² to find 44².
3. 3.Use (a − b)² = a² − 2ab + b² to find 24².
4. 4.Use (a + b)(a − b) = a² − b² to find 81 × 79.
5. 5.Use (a + b)² = a² + 2ab + b² to find 84².
6. 6.If a + b = 5 and ab = 6, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 78².
8. 8.If a − b = 2 and ab = 63, what is a² + b²?
9. 9.If a + b = 4 and ab = 3, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 85².
11. 11.Use (a − b)² = a² − 2ab + b² to find 84².
12. 12.Find the value of x² − 2xy + y² when x = 5 and y = 3.
13. 13.Use a² − b² = (a + b)(a − b) to find 61² − 59².
14. 14.Use (a + b)² = a² + 2ab + b² to find 56².
15. 15.Use (a + b)(a − b) = a² − b² to find 36 × 24.
16. 16.Use a² − b² = (a + b)(a − b) to find 95² − 1².
17. 17.Find the value of x² − y² when x = 13 and y = 5.
18. 18.If a − b = 2 and ab = 3, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 82² − 39².
20. 20.Use (a − b)² = a² − 2ab + b² to find 19².
21. 21.Use (a − b)² = a² − 2ab + b² to find 15².
22. 22.If a − b = 5 and ab = 14, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 71 × 69.
24. 24.Find the value of x² + 2xy + y² when x = 10 and y = 1.
25. 25.Use (a + b)² = a² + 2ab + b² to find 89².
26. 26.Use (a + b)² = a² + 2ab + b² to find 52².
27. 27.Use a² − b² = (a + b)(a − b) to find 72² − 33².
28. 28.Use a² − b² = (a + b)(a − b) to find 21² − 2².
29. 29.If a + b = 11 and ab = 10, what is a² + b²?
30. 30.Find the value of x² − y² when x = 13 and y = 1.
31. 31.Use (a − b)² = a² − 2ab + b² to find 89².
32. 32.Use (a + b)(a − b) = a² − b² to find 31 × 29.
33. 33.Use (a + b)² = a² + 2ab + b² to find 11².
34. 34.Use a² − b² = (a + b)(a − b) to find 41² − 28².
35. 35.Use (a − b)² = a² − 2ab + b² to find 55².
36. 36.Use (a − b)² = a² − 2ab + b² to find 64².
37. 37.If a + b = 20 and ab = 99, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 94² − 45².
39. 39.Use a² − b² = (a + b)(a − b) to find 99² − 8².
40. 40.Use (a − b)² = a² − 2ab + b² to find 39².

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