Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 688 · 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 = 3.
2. 2.If a + b = 14 and ab = 48, what is a² + b²?
3. 3.Find the value of x² + 2xy + y² when x = 4 and y = 2.
4. 4.Use (a − b)² = a² − 2ab + b² to find 57².
5. 5.Use (a + b)² = a² + 2ab + b² to find 71².
6. 6.Use (a − b)² = a² − 2ab + b² to find 24².
7. 7.If a − b = 2 and ab = 15, what is a² + b²?
8. 8.If a − b = 3 and ab = 4, what is a² + b²?
9. 9.If a − b = 2 and ab = 80, what is a² + b²?
10. 10.If a − b = 9 and ab = 10, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 22 × 18.
12. 12.Find the value of x² + 2xy + y² when x = 10 and y = 2.
13. 13.Use a² − b² = (a + b)(a − b) to find 36² − 33².
14. 14.Use (a + b)(a − b) = a² − b² to find 37 × 23.
15. 15.Use (a + b)² = a² + 2ab + b² to find 81².
16. 16.Find the value of x² − 2xy + y² when x = 5 and y = 1.
17. 17.Use (a + b)(a − b) = a² − b² to find 52 × 48.
18. 18.Use (a − b)² = a² − 2ab + b² to find 66².
19. 19.Use a² − b² = (a + b)(a − b) to find 28² − 7².
20. 20.Find the value of x² − y² when x = 12 and y = 9.
21. 21.Find the value of x² − 2xy + y² when x = 11 and y = 6.
22. 22.Use (a + b)² = a² + 2ab + b² to find 29².
23. 23.Find the value of x² + 2xy + y² when x = 3 and y = 2.
24. 24.If a − b = 5 and ab = 14, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 43².
26. 26.Use (a + b)(a − b) = a² − b² to find 82 × 78.
27. 27.Use a² − b² = (a + b)(a − b) to find 79² − 43².
28. 28.Use (a + b)² = a² + 2ab + b² to find 101².
29. 29.Use a² − b² = (a + b)(a − b) to find 26² − 12².
30. 30.Find the value of x² − 2xy + y² when x = 3 and y = 2.
31. 31.Use (a + b)² = a² + 2ab + b² to find 92².
32. 32.Use (a + b)² = a² + 2ab + b² to find 59².
33. 33.Find the value of x² + 2xy + y² when x = 3 and y = 1.
34. 34.Use a² − b² = (a + b)(a − b) to find 99² − 13².
35. 35.Use (a + b)² = a² + 2ab + b² to find 17².
36. 36.Use (a + b)² = a² + 2ab + b² to find 91².
37. 37.Use (a − b)² = a² − 2ab + b² to find 23².
38. 38.If a + b = 6 and ab = 8, what is a² + b²?
39. 39.Find the value of x² − 2xy + y² when x = 15 and y = 7.
40. 40.Use (a + b)² = a² + 2ab + b² to find 11².

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