Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 925 · 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 74².
2. 2.If a − b = 1 and ab = 132, what is a² + b²?
3. 3.Find the value of x² − y² when x = 7 and y = 4.
4. 4.Use (a + b)² = a² + 2ab + b² to find 43².
5. 5.Use (a + b)² = a² + 2ab + b² to find 106².
6. 6.Use (a + b)(a − b) = a² − b² to find 76 × 64.
7. 7.If a + b = 5 and ab = 6, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 21².
9. 9.Use (a + b)² = a² + 2ab + b² to find 86².
10. 10.Use (a + b)(a − b) = a² − b² to find 99 × 81.
11. 11.Use (a + b)² = a² + 2ab + b² to find 56².
12. 12.Find the value of x² − y² when x = 10 and y = 3.
13. 13.Use (a − b)² = a² − 2ab + b² to find 34².
14. 14.Use (a + b)² = a² + 2ab + b² to find 68².
15. 15.Use (a + b)² = a² + 2ab + b² to find 36².
16. 16.Use a² − b² = (a + b)(a − b) to find 58² − 24².
17. 17.Use a² − b² = (a + b)(a − b) to find 65² − 50².
18. 18.Find the value of x² + 2xy + y² when x = 14 and y = 7.
19. 19.Use (a − b)² = a² − 2ab + b² to find 56².
20. 20.Use a² − b² = (a + b)(a − b) to find 74² − 12².
21. 21.If a + b = 12 and ab = 32, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 53².
23. 23.Find the value of x² − y² when x = 5 and y = 2.
24. 24.Use (a + b)(a − b) = a² − b² to find 95 × 85.
25. 25.Use (a + b)(a − b) = a² − b² to find 64 × 56.
26. 26.Use (a − b)² = a² − 2ab + b² to find 81².
27. 27.Use (a − b)² = a² − 2ab + b² to find 28².
28. 28.Use (a − b)² = a² − 2ab + b² to find 32².
29. 29.Use (a + b)² = a² + 2ab + b² to find 33².
30. 30.Use (a − b)² = a² − 2ab + b² to find 37².
31. 31.Use (a + b)² = a² + 2ab + b² to find 98².
32. 32.Use a² − b² = (a + b)(a − b) to find 74² − 64².
33. 33.Use (a + b)(a − b) = a² − b² to find 69 × 51.
34. 34.Use a² − b² = (a + b)(a − b) to find 41² − 5².
35. 35.Find the value of x² − 2xy + y² when x = 8 and y = 5.
36. 36.Find the value of x² − 2xy + y² when x = 14 and y = 2.
37. 37.If a + b = 3 and ab = 2, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 83².
39. 39.Use (a − b)² = a² − 2ab + b² to find 69².
40. 40.Use (a + b)² = a² + 2ab + b² to find 63².

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