Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 494 · 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 72².
2. 2.Use (a + b)(a − b) = a² − b² to find 85 × 75.
3. 3.Use (a − b)² = a² − 2ab + b² to find 97².
4. 4.If a − b = 3 and ab = 10, what is a² + b²?
5. 5.If a + b = 18 and ab = 80, what is a² + b²?
6. 6.If a − b = 4 and ab = 77, what is a² + b²?
7. 7.Find the value of x² − 2xy + y² when x = 12 and y = 10.
8. 8.Use (a + b)(a − b) = a² − b² to find 97 × 83.
9. 9.Find the value of x² − 2xy + y² when x = 3 and y = 1.
10. 10.Find the value of x² + 2xy + y² when x = 10 and y = 7.
11. 11.Use a² − b² = (a + b)(a − b) to find 88² − 68².
12. 12.Find the value of x² − y² when x = 4 and y = 3.
13. 13.Use (a + b)² = a² + 2ab + b² to find 36².
14. 14.Use (a + b)² = a² + 2ab + b² to find 84².
15. 15.Use (a + b)(a − b) = a² − b² to find 26 × 14.
16. 16.Use (a − b)² = a² − 2ab + b² to find 16².
17. 17.Find the value of x² − y² when x = 7 and y = 2.
18. 18.Use (a + b)² = a² + 2ab + b² to find 81².
19. 19.Use (a + b)(a − b) = a² − b² to find 82 × 78.
20. 20.Use (a + b)² = a² + 2ab + b² to find 13².
21. 21.Use (a − b)² = a² − 2ab + b² to find 74².
22. 22.If a − b = 1 and ab = 6, what is a² + b²?
23. 23.Find the value of x² − 2xy + y² when x = 4 and y = 1.
24. 24.Find the value of x² − 2xy + y² when x = 7 and y = 4.
25. 25.Use a² − b² = (a + b)(a − b) to find 34² − 2².
26. 26.If a + b = 15 and ab = 36, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 86 × 74.
28. 28.Use a² − b² = (a + b)(a − b) to find 56² − 19².
29. 29.Use (a + b)(a − b) = a² − b² to find 36 × 24.
30. 30.Use a² − b² = (a + b)(a − b) to find 62² − 5².
31. 31.Use (a + b)² = a² + 2ab + b² to find 68².
32. 32.Use (a + b)(a − b) = a² − b² to find 71 × 69.
33. 33.If a − b = 2 and ab = 120, what is a² + b²?
34. 34.Find the value of x² + 2xy + y² when x = 11 and y = 9.
35. 35.Use (a + b)(a − b) = a² − b² to find 61 × 59.
36. 36.Use (a + b)(a − b) = a² − b² to find 49 × 31.
37. 37.Use a² − b² = (a + b)(a − b) to find 37² − 30².
38. 38.Find the value of x² + 2xy + y² when x = 9 and y = 5.
39. 39.Use (a − b)² = a² − 2ab + b² to find 41².
40. 40.Use (a − b)² = a² − 2ab + b² to find 11².

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