Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 542 · 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 15².
2. 2.Use (a + b)² = a² + 2ab + b² to find 51².
3. 3.Use (a + b)(a − b) = a² − b² to find 48 × 32.
4. 4.Use a² − b² = (a + b)(a − b) to find 29² − 24².
5. 5.Use a² − b² = (a + b)(a − b) to find 53² − 43².
6. 6.Use (a + b)² = a² + 2ab + b² to find 53².
7. 7.Use (a + b)² = a² + 2ab + b² to find 86².
8. 8.If a + b = 11 and ab = 24, what is a² + b²?
9. 9.Use (a + b)(a − b) = a² − b² to find 88 × 72.
10. 10.Use (a − b)² = a² − 2ab + b² to find 12².
11. 11.Use a² − b² = (a + b)(a − b) to find 26² − 25².
12. 12.Use (a − b)² = a² − 2ab + b² to find 13².
13. 13.Find the value of x² − 2xy + y² when x = 3 and y = 2.
14. 14.Find the value of x² + 2xy + y² when x = 4 and y = 2.
15. 15.Use (a + b)(a − b) = a² − b² to find 35 × 25.
16. 16.Use (a − b)² = a² − 2ab + b² to find 14².
17. 17.Find the value of x² − y² when x = 3 and y = 1.
18. 18.Use a² − b² = (a + b)(a − b) to find 71² − 48².
19. 19.Use (a − b)² = a² − 2ab + b² to find 39².
20. 20.Find the value of x² + 2xy + y² when x = 3 and y = 2.
21. 21.Use (a − b)² = a² − 2ab + b² to find 46².
22. 22.Use (a − b)² = a² − 2ab + b² to find 99².
23. 23.Use (a + b)(a − b) = a² − b² to find 81 × 79.
24. 24.Find the value of x² − 2xy + y² when x = 6 and y = 4.
25. 25.If a + b = 13 and ab = 22, what is a² + b²?
26. 26.Find the value of x² + 2xy + y² when x = 14 and y = 1.
27. 27.Use a² − b² = (a + b)(a − b) to find 96² − 73².
28. 28.If a − b = 3 and ab = 10, what is a² + b²?
29. 29.Find the value of x² + 2xy + y² when x = 4 and y = 3.
30. 30.Use (a + b)² = a² + 2ab + b² to find 76².
31. 31.Find the value of x² − 2xy + y² when x = 12 and y = 1.
32. 32.Use (a − b)² = a² − 2ab + b² to find 35².
33. 33.Use (a + b)² = a² + 2ab + b² to find 32².
34. 34.Find the value of x² − 2xy + y² when x = 3 and y = 1.
35. 35.Use (a − b)² = a² − 2ab + b² to find 49².
36. 36.Use (a + b)² = a² + 2ab + b² to find 109².
37. 37.Use (a − b)² = a² − 2ab + b² to find 69².
38. 38.Find the value of x² − 2xy + y² when x = 11 and y = 7.
39. 39.Find the value of x² + 2xy + y² when x = 15 and y = 11.
40. 40.Use (a + b)(a − b) = a² − b² to find 79 × 61.

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