Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 309 · 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 = 6 and y = 2.
2. 2.Use (a − b)² = a² − 2ab + b² to find 77².
3. 3.Use (a + b)² = a² + 2ab + b² to find 18².
4. 4.Use a² − b² = (a + b)(a − b) to find 99² − 1².
5. 5.Use (a + b)(a − b) = a² − b² to find 51 × 49.
6. 6.Use (a + b)(a − b) = a² − b² to find 87 × 73.
7. 7.Use (a − b)² = a² − 2ab + b² to find 37².
8. 8.Use (a − b)² = a² − 2ab + b² to find 39².
9. 9.Use (a + b)² = a² + 2ab + b² to find 24².
10. 10.If a + b = 3 and ab = 2, what is a² + b²?
11. 11.If a + b = 5 and ab = 4, what is a² + b²?
12. 12.Use (a + b)² = a² + 2ab + b² to find 17².
13. 13.Use a² − b² = (a + b)(a − b) to find 42² − 20².
14. 14.Find the value of x² − y² when x = 5 and y = 2.
15. 15.Use (a + b)(a − b) = a² − b² to find 65 × 55.
16. 16.Use (a + b)² = a² + 2ab + b² to find 72².
17. 17.Use a² − b² = (a + b)(a − b) to find 42² − 12².
18. 18.Use (a − b)² = a² − 2ab + b² to find 54².
19. 19.Find the value of x² + 2xy + y² when x = 13 and y = 7.
20. 20.Find the value of x² − 2xy + y² when x = 15 and y = 7.
21. 21.Use (a − b)² = a² − 2ab + b² to find 88².
22. 22.Use a² − b² = (a + b)(a − b) to find 43² − 31².
23. 23.Use (a + b)² = a² + 2ab + b² to find 26².
24. 24.Use a² − b² = (a + b)(a − b) to find 29² − 16².
25. 25.Use (a − b)² = a² − 2ab + b² to find 31².
26. 26.Use (a + b)² = a² + 2ab + b² to find 105².
27. 27.Use (a + b)² = a² + 2ab + b² to find 48².
28. 28.Use (a − b)² = a² − 2ab + b² to find 55².
29. 29.If a + b = 5 and ab = 6, what is a² + b²?
30. 30.Use a² − b² = (a + b)(a − b) to find 62² − 51².
31. 31.Use (a + b)² = a² + 2ab + b² to find 11².
32. 32.If a + b = 9 and ab = 14, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 69².
34. 34.Use (a − b)² = a² − 2ab + b² to find 19².
35. 35.Use (a − b)² = a² − 2ab + b² to find 35².
36. 36.Find the value of x² − 2xy + y² when x = 15 and y = 12.
37. 37.Use (a − b)² = a² − 2ab + b² to find 84².
38. 38.Use (a + b)(a − b) = a² − b² to find 59 × 41.
39. 39.Use (a + b)² = a² + 2ab + b² to find 69².
40. 40.Use (a − b)² = a² − 2ab + b² to find 46².

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