Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 527 · 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 68².
2. 2.Use (a − b)² = a² − 2ab + b² to find 82².
3. 3.Find the value of x² + 2xy + y² when x = 12 and y = 6.
4. 4.Use (a + b)(a − b) = a² − b² to find 99 × 81.
5. 5.Use (a + b)(a − b) = a² − b² to find 74 × 66.
6. 6.Use (a − b)² = a² − 2ab + b² to find 48².
7. 7.Find the value of x² − 2xy + y² when x = 14 and y = 11.
8. 8.If a + b = 6 and ab = 8, what is a² + b²?
9. 9.Use (a + b)² = a² + 2ab + b² to find 89².
10. 10.Use (a + b)(a − b) = a² − b² to find 77 × 63.
11. 11.Find the value of x² − y² when x = 15 and y = 11.
12. 12.Use a² − b² = (a + b)(a − b) to find 37² − 14².
13. 13.Use (a − b)² = a² − 2ab + b² to find 16².
14. 14.Use a² − b² = (a + b)(a − b) to find 91² − 18².
15. 15.Use (a + b)² = a² + 2ab + b² to find 36².
16. 16.Use (a − b)² = a² − 2ab + b² to find 15².
17. 17.If a − b = 1 and ab = 2, what is a² + b²?
18. 18.Use (a + b)(a − b) = a² − b² to find 72 × 68.
19. 19.Use (a − b)² = a² − 2ab + b² to find 58².
20. 20.Use a² − b² = (a + b)(a − b) to find 95² − 78².
21. 21.Use (a + b)(a − b) = a² − b² to find 95 × 85.
22. 22.Use a² − b² = (a + b)(a − b) to find 34² − 27².
23. 23.Use (a + b)² = a² + 2ab + b² to find 76².
24. 24.Use a² − b² = (a + b)(a − b) to find 27² − 13².
25. 25.Find the value of x² − 2xy + y² when x = 13 and y = 6.
26. 26.If a + b = 16 and ab = 60, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 83 × 77.
28. 28.Use (a + b)² = a² + 2ab + b² to find 22².
29. 29.Use a² − b² = (a + b)(a − b) to find 74² − 7².
30. 30.Use a² − b² = (a + b)(a − b) to find 62² − 26².
31. 31.Use (a − b)² = a² − 2ab + b² to find 47².
32. 32.If a − b = 5 and ab = 6, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 101 × 99.
34. 34.If a − b = 2 and ab = 3, what is a² + b²?
35. 35.Find the value of x² − y² when x = 12 and y = 8.
36. 36.Use a² − b² = (a + b)(a − b) to find 52² − 37².
37. 37.Find the value of x² + 2xy + y² when x = 15 and y = 4.
38. 38.Use a² − b² = (a + b)(a − b) to find 62² − 30².
39. 39.Use (a + b)² = a² + 2ab + b² to find 53².
40. 40.Use (a + b)(a − b) = a² − b² to find 73 × 67.

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