Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 839 · 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 38².
2. 2.Use a² − b² = (a + b)(a − b) to find 31² − 24².
3. 3.Find the value of x² − 2xy + y² when x = 4 and y = 2.
4. 4.Use (a + b)² = a² + 2ab + b² to find 15².
5. 5.Find the value of x² + 2xy + y² when x = 5 and y = 1.
6. 6.Use a² − b² = (a + b)(a − b) to find 36² − 33².
7. 7.Use (a − b)² = a² − 2ab + b² to find 36².
8. 8.Use (a + b)² = a² + 2ab + b² to find 47².
9. 9.Use (a + b)(a − b) = a² − b² to find 24 × 16.
10. 10.Use a² − b² = (a + b)(a − b) to find 39² − 15².
11. 11.Find the value of x² + 2xy + y² when x = 4 and y = 1.
12. 12.Use (a + b)(a − b) = a² − b² to find 34 × 26.
13. 13.Find the value of x² + 2xy + y² when x = 10 and y = 4.
14. 14.Find the value of x² − y² when x = 14 and y = 1.
15. 15.If a − b = 3 and ab = 54, what is a² + b²?
16. 16.If a − b = 3 and ab = 40, what is a² + b²?
17. 17.Use (a + b)(a − b) = a² − b² to find 81 × 79.
18. 18.Find the value of x² + 2xy + y² when x = 8 and y = 1.
19. 19.Use (a + b)² = a² + 2ab + b² to find 36².
20. 20.Use a² − b² = (a + b)(a − b) to find 98² − 7².
21. 21.If a + b = 4 and ab = 3, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 33² − 5².
23. 23.Use (a + b)² = a² + 2ab + b² to find 58².
24. 24.Find the value of x² − y² when x = 10 and y = 6.
25. 25.Use (a − b)² = a² − 2ab + b² to find 19².
26. 26.Use (a + b)² = a² + 2ab + b² to find 42².
27. 27.Find the value of x² + 2xy + y² when x = 6 and y = 1.
28. 28.Use a² − b² = (a + b)(a − b) to find 72² − 22².
29. 29.Find the value of x² − 2xy + y² when x = 3 and y = 2.
30. 30.Use a² − b² = (a + b)(a − b) to find 43² − 35².
31. 31.Use (a + b)(a − b) = a² − b² to find 85 × 75.
32. 32.Use (a − b)² = a² − 2ab + b² to find 35².
33. 33.Use (a − b)² = a² − 2ab + b² to find 15².
34. 34.Find the value of x² + 2xy + y² when x = 4 and y = 2.
35. 35.Use (a + b)(a − b) = a² − b² to find 22 × 18.
36. 36.Find the value of x² − y² when x = 8 and y = 1.
37. 37.Use (a − b)² = a² − 2ab + b² to find 21².
38. 38.If a − b = 10 and ab = 24, what is a² + b²?
39. 39.Use (a + b)² = a² + 2ab + b² to find 87².
40. 40.Find the value of x² − y² when x = 15 and y = 3.

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