Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 900 · 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 27² − 3².
2. 2.Use (a + b)² = a² + 2ab + b² to find 23².
3. 3.Find the value of x² − 2xy + y² when x = 14 and y = 11.
4. 4.Use (a + b)(a − b) = a² − b² to find 51 × 49.
5. 5.Find the value of x² − 2xy + y² when x = 11 and y = 3.
6. 6.Use (a + b)(a − b) = a² − b² to find 22 × 18.
7. 7.Find the value of x² − y² when x = 15 and y = 7.
8. 8.Use (a − b)² = a² − 2ab + b² to find 55².
9. 9.Use a² − b² = (a + b)(a − b) to find 71² − 24².
10. 10.Use a² − b² = (a + b)(a − b) to find 91² − 68².
11. 11.If a + b = 14 and ab = 33, what is a² + b²?
12. 12.Find the value of x² − 2xy + y² when x = 15 and y = 4.
13. 13.Use (a + b)(a − b) = a² − b² to find 59 × 41.
14. 14.Use (a + b)² = a² + 2ab + b² to find 45².
15. 15.Use a² − b² = (a + b)(a − b) to find 91² − 64².
16. 16.Use (a − b)² = a² − 2ab + b² to find 28².
17. 17.If a + b = 4 and ab = 3, what is a² + b²?
18. 18.If a + b = 13 and ab = 40, what is a² + b²?
19. 19.If a + b = 6 and ab = 5, what is a² + b²?
20. 20.Find the value of x² − 2xy + y² when x = 7 and y = 6.
21. 21.If a − b = 2 and ab = 24, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 57 × 43.
23. 23.Use (a + b)² = a² + 2ab + b² to find 13².
24. 24.If a + b = 9 and ab = 14, what is a² + b²?
25. 25.Find the value of x² − 2xy + y² when x = 15 and y = 3.
26. 26.Use (a − b)² = a² − 2ab + b² to find 56².
27. 27.Use (a + b)(a − b) = a² − b² to find 63 × 57.
28. 28.Use a² − b² = (a + b)(a − b) to find 60² − 5².
29. 29.Use a² − b² = (a + b)(a − b) to find 20² − 18².
30. 30.Use (a + b)(a − b) = a² − b² to find 39 × 21.
31. 31.Use (a + b)(a − b) = a² − b² to find 28 × 12.
32. 32.Use (a − b)² = a² − 2ab + b² to find 81².
33. 33.Use a² − b² = (a + b)(a − b) to find 83² − 12².
34. 34.Use (a + b)(a − b) = a² − b² to find 47 × 33.
35. 35.Find the value of x² + 2xy + y² when x = 4 and y = 2.
36. 36.Use (a + b)² = a² + 2ab + b² to find 91².
37. 37.Find the value of x² + 2xy + y² when x = 9 and y = 8.
38. 38.Use (a + b)(a − b) = a² − b² to find 79 × 61.
39. 39.If a + b = 9 and ab = 18, what is a² + b²?
40. 40.Use (a − b)² = a² − 2ab + b² to find 89².

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