Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 359 · 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 15².
2. 2.If a − b = 1 and ab = 6, what is a² + b²?
3. 3.Find the value of x² + 2xy + y² when x = 3 and y = 2.
4. 4.Use (a − b)² = a² − 2ab + b² to find 79².
5. 5.Find the value of x² − 2xy + y² when x = 4 and y = 1.
6. 6.Use (a + b)² = a² + 2ab + b² to find 63².
7. 7.Use (a + b)² = a² + 2ab + b² to find 33².
8. 8.Use (a + b)² = a² + 2ab + b² to find 29².
9. 9.Find the value of x² − y² when x = 12 and y = 7.
10. 10.Use (a − b)² = a² − 2ab + b² to find 65².
11. 11.Find the value of x² − y² when x = 8 and y = 1.
12. 12.Use (a + b)² = a² + 2ab + b² to find 13².
13. 13.Use a² − b² = (a + b)(a − b) to find 63² − 6².
14. 14.Use (a − b)² = a² − 2ab + b² to find 61².
15. 15.Use (a − b)² = a² − 2ab + b² to find 47².
16. 16.If a − b = 8 and ab = 9, what is a² + b²?
17. 17.Find the value of x² − y² when x = 14 and y = 6.
18. 18.Use a² − b² = (a + b)(a − b) to find 57² − 5².
19. 19.Use a² − b² = (a + b)(a − b) to find 80² − 69².
20. 20.If a + b = 3 and ab = 2, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 24 × 16.
22. 22.Use (a + b)² = a² + 2ab + b² to find 75².
23. 23.Find the value of x² + 2xy + y² when x = 8 and y = 1.
24. 24.Use (a + b)² = a² + 2ab + b² to find 26².
25. 25.Use (a + b)² = a² + 2ab + b² to find 25².
26. 26.Use (a − b)² = a² − 2ab + b² to find 26².
27. 27.Use (a − b)² = a² − 2ab + b² to find 92².
28. 28.If a + b = 14 and ab = 48, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 47².
30. 30.Use a² − b² = (a + b)(a − b) to find 43² − 10².
31. 31.Use (a − b)² = a² − 2ab + b² to find 17².
32. 32.Use (a − b)² = a² − 2ab + b² to find 31².
33. 33.Use (a + b)² = a² + 2ab + b² to find 87².
34. 34.Use (a + b)² = a² + 2ab + b² to find 86².
35. 35.Use (a + b)(a − b) = a² − b² to find 34 × 26.
36. 36.Use (a − b)² = a² − 2ab + b² to find 87².
37. 37.Find the value of x² − 2xy + y² when x = 5 and y = 3.
38. 38.If a + b = 20 and ab = 96, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 27 × 13.
40. 40.Use (a + b)(a − b) = a² − b² to find 95 × 85.

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