Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 196 · 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)(a − b) = a² − b² to find 66 × 54.
2. 2.Use (a + b)(a − b) = a² − b² to find 73 × 67.
3. 3.Find the value of x² − y² when x = 11 and y = 8.
4. 4.Use a² − b² = (a + b)(a − b) to find 54² − 15².
5. 5.Find the value of x² − y² when x = 11 and y = 1.
6. 6.If a − b = 3 and ab = 108, what is a² + b²?
7. 7.Find the value of x² − y² when x = 13 and y = 2.
8. 8.Use (a + b)(a − b) = a² − b² to find 56 × 44.
9. 9.Use a² − b² = (a + b)(a − b) to find 91² − 35².
10. 10.Use (a − b)² = a² − 2ab + b² to find 56².
11. 11.Find the value of x² − 2xy + y² when x = 15 and y = 13.
12. 12.Find the value of x² − y² when x = 13 and y = 10.
13. 13.Use (a + b)(a − b) = a² − b² to find 71 × 69.
14. 14.Find the value of x² − 2xy + y² when x = 12 and y = 5.
15. 15.Use (a + b)(a − b) = a² − b² to find 25 × 15.
16. 16.Use (a − b)² = a² − 2ab + b² to find 71².
17. 17.Use (a + b)(a − b) = a² − b² to find 83 × 77.
18. 18.Find the value of x² − 2xy + y² when x = 3 and y = 2.
19. 19.Use a² − b² = (a + b)(a − b) to find 40² − 23².
20. 20.Use (a + b)² = a² + 2ab + b² to find 13².
21. 21.Find the value of x² − 2xy + y² when x = 5 and y = 4.
22. 22.Use a² − b² = (a + b)(a − b) to find 24² − 5².
23. 23.Use (a + b)² = a² + 2ab + b² to find 49².
24. 24.Use (a − b)² = a² − 2ab + b² to find 46².
25. 25.If a + b = 4 and ab = 3, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 19².
27. 27.Use a² − b² = (a + b)(a − b) to find 93² − 59².
28. 28.Find the value of x² − y² when x = 12 and y = 7.
29. 29.Use (a + b)² = a² + 2ab + b² to find 25².
30. 30.Use (a − b)² = a² − 2ab + b² to find 23².
31. 31.If a − b = 1 and ab = 20, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 44² − 6².
33. 33.Use a² − b² = (a + b)(a − b) to find 25² − 7².
34. 34.Use a² − b² = (a + b)(a − b) to find 76² − 70².
35. 35.Use a² − b² = (a + b)(a − b) to find 28² − 24².
36. 36.Use a² − b² = (a + b)(a − b) to find 71² − 62².
37. 37.Find the value of x² − y² when x = 9 and y = 2.
38. 38.Use (a − b)² = a² − 2ab + b² to find 64².
39. 39.Use (a + b)(a − b) = a² − b² to find 102 × 98.
40. 40.Use (a + b)² = a² + 2ab + b² to find 41².

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