Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 305 · 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)² = a² + 2ab + b² to find 29².
2. 2.Find the value of x² − 2xy + y² when x = 10 and y = 2.
3. 3.Find the value of x² + 2xy + y² when x = 15 and y = 3.
4. 4.Use a² − b² = (a + b)(a − b) to find 53² − 9².
5. 5.Use (a + b)(a − b) = a² − b² to find 42 × 38.
6. 6.Use (a + b)² = a² + 2ab + b² to find 25².
7. 7.Use (a − b)² = a² − 2ab + b² to find 36².
8. 8.Use (a + b)(a − b) = a² − b² to find 92 × 88.
9. 9.If a + b = 12 and ab = 32, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 79².
11. 11.Use (a − b)² = a² − 2ab + b² to find 73².
12. 12.Use (a + b)(a − b) = a² − b² to find 81 × 79.
13. 13.Use a² − b² = (a + b)(a − b) to find 49² − 19².
14. 14.Use (a + b)² = a² + 2ab + b² to find 42².
15. 15.If a + b = 17 and ab = 66, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 18².
17. 17.Find the value of x² + 2xy + y² when x = 10 and y = 9.
18. 18.Use (a + b)(a − b) = a² − b² to find 41 × 39.
19. 19.Use (a − b)² = a² − 2ab + b² to find 84².
20. 20.If a − b = 1 and ab = 30, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 21².
22. 22.Use (a − b)² = a² − 2ab + b² to find 28².
23. 23.Use (a + b)(a − b) = a² − b² to find 31 × 29.
24. 24.Use (a + b)² = a² + 2ab + b² to find 106².
25. 25.Use (a − b)² = a² − 2ab + b² to find 65².
26. 26.Use (a − b)² = a² − 2ab + b² to find 96².
27. 27.Find the value of x² + 2xy + y² when x = 4 and y = 2.
28. 28.Find the value of x² + 2xy + y² when x = 12 and y = 9.
29. 29.Find the value of x² + 2xy + y² when x = 15 and y = 9.
30. 30.Use (a − b)² = a² − 2ab + b² to find 15².
31. 31.Use (a + b)² = a² + 2ab + b² to find 39².
32. 32.Use (a + b)(a − b) = a² − b² to find 72 × 68.
33. 33.If a + b = 4 and ab = 3, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 72².
35. 35.Use (a + b)² = a² + 2ab + b² to find 103².
36. 36.Use a² − b² = (a + b)(a − b) to find 96² − 42².
37. 37.If a + b = 3 and ab = 2, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 69².
39. 39.If a − b = 4 and ab = 60, what is a² + b²?
40. 40.Find the value of x² − 2xy + y² when x = 3 and y = 1.

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