Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 403 · 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 a² − b² = (a + b)(a − b) to find 25² − 5².
2. 2.Use (a + b)(a − b) = a² − b² to find 99 × 81.
3. 3.Use (a − b)² = a² − 2ab + b² to find 49².
4. 4.Use (a + b)² = a² + 2ab + b² to find 74².
5. 5.Use (a + b)² = a² + 2ab + b² to find 79².
6. 6.Use (a − b)² = a² − 2ab + b² to find 93².
7. 7.Use (a + b)² = a² + 2ab + b² to find 35².
8. 8.Use (a − b)² = a² − 2ab + b² to find 18².
9. 9.Use (a + b)(a − b) = a² − b² to find 38 × 22.
10. 10.Use a² − b² = (a + b)(a − b) to find 21² − 16².
11. 11.Use (a + b)² = a² + 2ab + b² to find 34².
12. 12.Use (a + b)² = a² + 2ab + b² to find 22².
13. 13.If a − b = 1 and ab = 20, what is a² + b²?
14. 14.If a − b = 7 and ab = 8, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 82².
16. 16.Use (a + b)² = a² + 2ab + b² to find 65².
17. 17.Use (a + b)² = a² + 2ab + b² to find 18².
18. 18.Find the value of x² − y² when x = 10 and y = 5.
19. 19.Use (a + b)² = a² + 2ab + b² to find 62².
20. 20.Use (a + b)(a − b) = a² − b² to find 23 × 17.
21. 21.If a + b = 6 and ab = 8, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 27².
23. 23.If a − b = 1 and ab = 2, what is a² + b²?
24. 24.If a + b = 14 and ab = 24, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 13².
26. 26.If a + b = 3 and ab = 2, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 62² − 49².
28. 28.Use (a + b)² = a² + 2ab + b² to find 47².
29. 29.Use (a + b)(a − b) = a² − b² to find 77 × 63.
30. 30.If a + b = 19 and ab = 90, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 68 × 52.
32. 32.Find the value of x² + 2xy + y² when x = 14 and y = 11.
33. 33.Find the value of x² − y² when x = 3 and y = 1.
34. 34.If a − b = 10 and ab = 24, what is a² + b²?
35. 35.If a − b = 3 and ab = 4, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 30² − 23².
37. 37.Use (a − b)² = a² − 2ab + b² to find 98².
38. 38.Use (a + b)² = a² + 2ab + b² to find 36².
39. 39.Use (a + b)² = a² + 2ab + b² to find 104².
40. 40.Use a² − b² = (a + b)(a − b) to find 24² − 5².

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