Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 681 · 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 − y² when x = 5 and y = 4.
2. 2.Use (a − b)² = a² − 2ab + b² to find 64².
3. 3.Use (a + b)² = a² + 2ab + b² to find 29².
4. 4.Find the value of x² − 2xy + y² when x = 5 and y = 4.
5. 5.Use (a − b)² = a² − 2ab + b² to find 22².
6. 6.Use (a + b)(a − b) = a² − b² to find 69 × 51.
7. 7.Find the value of x² − y² when x = 5 and y = 1.
8. 8.Use (a + b)² = a² + 2ab + b² to find 48².
9. 9.Use (a + b)² = a² + 2ab + b² to find 56².
10. 10.Use (a − b)² = a² − 2ab + b² to find 89².
11. 11.Find the value of x² − y² when x = 8 and y = 3.
12. 12.Use (a + b)(a − b) = a² − b² to find 71 × 69.
13. 13.Find the value of x² + 2xy + y² when x = 7 and y = 1.
14. 14.Use (a − b)² = a² − 2ab + b² to find 66².
15. 15.Use (a + b)² = a² + 2ab + b² to find 49².
16. 16.Use a² − b² = (a + b)(a − b) to find 64² − 8².
17. 17.If a + b = 6 and ab = 5, what is a² + b²?
18. 18.Use (a + b)² = a² + 2ab + b² to find 37².
19. 19.Use (a + b)² = a² + 2ab + b² to find 35².
20. 20.Use (a − b)² = a² − 2ab + b² to find 34².
21. 21.If a − b = 8 and ab = 33, what is a² + b²?
22. 22.Find the value of x² + 2xy + y² when x = 13 and y = 6.
23. 23.Use (a + b)(a − b) = a² − b² to find 38 × 22.
24. 24.If a − b = 4 and ab = 12, what is a² + b²?
25. 25.Find the value of x² − y² when x = 12 and y = 9.
26. 26.Find the value of x² − y² when x = 10 and y = 4.
27. 27.If a − b = 1 and ab = 110, what is a² + b²?
28. 28.Find the value of x² − 2xy + y² when x = 3 and y = 2.
29. 29.If a + b = 15 and ab = 50, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 69².
31. 31.Use (a − b)² = a² − 2ab + b² to find 13².
32. 32.Use (a + b)(a − b) = a² − b² to find 24 × 16.
33. 33.Use (a + b)² = a² + 2ab + b² to find 36².
34. 34.Use a² − b² = (a + b)(a − b) to find 65² − 40².
35. 35.Use (a − b)² = a² − 2ab + b² to find 63².
36. 36.Use (a + b)² = a² + 2ab + b² to find 59².
37. 37.Use (a + b)² = a² + 2ab + b² to find 41².
38. 38.Find the value of x² − y² when x = 9 and y = 1.
39. 39.Use (a − b)² = a² − 2ab + b² to find 58².
40. 40.If a + b = 14 and ab = 40, what is a² + b²?

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