Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 401 · 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 73² − 55².
2. 2.Use (a + b)² = a² + 2ab + b² to find 16².
3. 3.Find the value of x² − 2xy + y² when x = 11 and y = 8.
4. 4.Use a² − b² = (a + b)(a − b) to find 21² − 18².
5. 5.Use (a − b)² = a² − 2ab + b² to find 69².
6. 6.Use (a + b)(a − b) = a² − b² to find 23 × 17.
7. 7.Use (a + b)² = a² + 2ab + b² to find 61².
8. 8.If a − b = 3 and ab = 40, what is a² + b²?
9. 9.Find the value of x² − 2xy + y² when x = 14 and y = 5.
10. 10.Use a² − b² = (a + b)(a − b) to find 64² − 6².
11. 11.Use (a + b)(a − b) = a² − b² to find 57 × 43.
12. 12.If a − b = 3 and ab = 4, what is a² + b²?
13. 13.If a + b = 7 and ab = 12, what is a² + b²?
14. 14.If a + b = 5 and ab = 4, what is a² + b²?
15. 15.Find the value of x² + 2xy + y² when x = 10 and y = 8.
16. 16.Find the value of x² + 2xy + y² when x = 14 and y = 6.
17. 17.Find the value of x² + 2xy + y² when x = 5 and y = 1.
18. 18.Use (a + b)² = a² + 2ab + b² to find 18².
19. 19.Use (a − b)² = a² − 2ab + b² to find 51².
20. 20.Use (a + b)² = a² + 2ab + b² to find 109².
21. 21.Use (a + b)² = a² + 2ab + b² to find 51².
22. 22.If a + b = 16 and ab = 48, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 21² − 3².
24. 24.Use (a − b)² = a² − 2ab + b² to find 22².
25. 25.Use (a + b)² = a² + 2ab + b² to find 28².
26. 26.Use (a + b)(a − b) = a² − b² to find 48 × 32.
27. 27.Find the value of x² + 2xy + y² when x = 9 and y = 5.
28. 28.Use a² − b² = (a + b)(a − b) to find 40² − 20².
29. 29.Use (a + b)² = a² + 2ab + b² to find 19².
30. 30.Use (a + b)² = a² + 2ab + b² to find 94².
31. 31.If a + b = 12 and ab = 27, what is a² + b²?
32. 32.Use (a − b)² = a² − 2ab + b² to find 92².
33. 33.Use (a − b)² = a² − 2ab + b² to find 35².
34. 34.Use a² − b² = (a + b)(a − b) to find 43² − 29².
35. 35.Use (a + b)(a − b) = a² − b² to find 95 × 85.
36. 36.Use (a + b)(a − b) = a² − b² to find 53 × 47.
37. 37.Use (a + b)(a − b) = a² − b² to find 56 × 44.
38. 38.Find the value of x² − 2xy + y² when x = 11 and y = 7.
39. 39.Use (a + b)² = a² + 2ab + b² to find 68².
40. 40.Use (a + b)(a − b) = a² − b² to find 46 × 34.

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