Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 945 · 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 85 × 75.
2. 2.Use (a + b)² = a² + 2ab + b² to find 11².
3. 3.If a + b = 3 and ab = 2, what is a² + b²?
4. 4.If a − b = 5 and ab = 6, what is a² + b²?
5. 5.Use (a − b)² = a² − 2ab + b² to find 36².
6. 6.Find the value of x² − y² when x = 5 and y = 1.
7. 7.Use (a + b)(a − b) = a² − b² to find 55 × 45.
8. 8.Use (a − b)² = a² − 2ab + b² to find 65².
9. 9.Use a² − b² = (a + b)(a − b) to find 20² − 5².
10. 10.Use (a + b)(a − b) = a² − b² to find 99 × 81.
11. 11.Use (a − b)² = a² − 2ab + b² to find 66².
12. 12.If a + b = 11 and ab = 30, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 16².
14. 14.Use a² − b² = (a + b)(a − b) to find 37² − 2².
15. 15.Use a² − b² = (a + b)(a − b) to find 92² − 82².
16. 16.If a − b = 10 and ab = 11, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 27² − 14².
18. 18.If a − b = 2 and ab = 3, what is a² + b²?
19. 19.Find the value of x² − y² when x = 10 and y = 1.
20. 20.Find the value of x² + 2xy + y² when x = 5 and y = 3.
21. 21.Use (a + b)(a − b) = a² − b² to find 47 × 33.
22. 22.Find the value of x² + 2xy + y² when x = 11 and y = 7.
23. 23.Find the value of x² + 2xy + y² when x = 13 and y = 5.
24. 24.Use (a + b)² = a² + 2ab + b² to find 36².
25. 25.Find the value of x² − 2xy + y² when x = 10 and y = 7.
26. 26.If a − b = 1 and ab = 2, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 61 × 59.
28. 28.Use a² − b² = (a + b)(a − b) to find 62² − 40².
29. 29.Use (a − b)² = a² − 2ab + b² to find 18².
30. 30.If a − b = 3 and ab = 4, what is a² + b²?
31. 31.If a + b = 11 and ab = 24, what is a² + b²?
32. 32.Find the value of x² + 2xy + y² when x = 4 and y = 1.
33. 33.Use (a − b)² = a² − 2ab + b² to find 64².
34. 34.If a + b = 10 and ab = 21, what is a² + b²?
35. 35.Use (a + b)² = a² + 2ab + b² to find 56².
36. 36.Use (a − b)² = a² − 2ab + b² to find 74².
37. 37.If a + b = 15 and ab = 50, what is a² + b²?
38. 38.If a + b = 11 and ab = 28, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 29² − 12².
40. 40.Use a² − b² = (a + b)(a − b) to find 85² − 6².

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