Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 350 · 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.If a − b = 7 and ab = 8, what is a² + b²?
2. 2.Find the value of x² − y² when x = 8 and y = 3.
3. 3.Use (a + b)² = a² + 2ab + b² to find 88².
4. 4.Use (a − b)² = a² − 2ab + b² to find 67².
5. 5.Use (a + b)(a − b) = a² − b² to find 32 × 28.
6. 6.Use (a − b)² = a² − 2ab + b² to find 74².
7. 7.Use (a + b)(a − b) = a² − b² to find 79 × 61.
8. 8.Use a² − b² = (a + b)(a − b) to find 58² − 53².
9. 9.If a + b = 22 and ab = 120, what is a² + b²?
10. 10.If a − b = 1 and ab = 72, what is a² + b²?
11. 11.Use a² − b² = (a + b)(a − b) to find 31² − 23².
12. 12.Use (a − b)² = a² − 2ab + b² to find 85².
13. 13.Use (a + b)(a − b) = a² − b² to find 68 × 52.
14. 14.Find the value of x² + 2xy + y² when x = 5 and y = 4.
15. 15.Find the value of x² + 2xy + y² when x = 11 and y = 2.
16. 16.Use (a − b)² = a² − 2ab + b² to find 91².
17. 17.If a − b = 2 and ab = 35, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 69² − 10².
19. 19.If a + b = 6 and ab = 8, what is a² + b²?
20. 20.Use (a − b)² = a² − 2ab + b² to find 37².
21. 21.Find the value of x² + 2xy + y² when x = 9 and y = 7.
22. 22.Find the value of x² + 2xy + y² when x = 10 and y = 6.
23. 23.Find the value of x² − y² when x = 3 and y = 2.
24. 24.Find the value of x² − 2xy + y² when x = 12 and y = 1.
25. 25.Use (a − b)² = a² − 2ab + b² to find 83².
26. 26.If a + b = 7 and ab = 12, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 46 × 34.
28. 28.If a + b = 8 and ab = 15, what is a² + b²?
29. 29.Use (a + b)(a − b) = a² − b² to find 38 × 22.
30. 30.Use (a + b)² = a² + 2ab + b² to find 15².
31. 31.Use (a − b)² = a² − 2ab + b² to find 27².
32. 32.Use (a − b)² = a² − 2ab + b² to find 96².
33. 33.Use (a + b)² = a² + 2ab + b² to find 25².
34. 34.If a + b = 11 and ab = 24, what is a² + b²?
35. 35.If a − b = 4 and ab = 21, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 57².
37. 37.Use (a + b)² = a² + 2ab + b² to find 102².
38. 38.Use (a − b)² = a² − 2ab + b² to find 13².
39. 39.If a − b = 2 and ab = 8, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 76².

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