Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 684 · 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 51².
2. 2.Use (a + b)² = a² + 2ab + b² to find 13².
3. 3.Use (a − b)² = a² − 2ab + b² to find 28².
4. 4.Find the value of x² − 2xy + y² when x = 6 and y = 1.
5. 5.If a − b = 1 and ab = 2, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 29².
7. 7.Use (a + b)(a − b) = a² − b² to find 55 × 45.
8. 8.Use (a + b)(a − b) = a² − b² to find 81 × 79.
9. 9.Use (a + b)² = a² + 2ab + b² to find 62².
10. 10.Use (a + b)² = a² + 2ab + b² to find 86².
11. 11.Use (a + b)² = a² + 2ab + b² to find 29².
12. 12.Use (a − b)² = a² − 2ab + b² to find 88².
13. 13.If a − b = 2 and ab = 8, what is a² + b²?
14. 14.If a + b = 13 and ab = 40, what is a² + b²?
15. 15.If a − b = 4 and ab = 45, what is a² + b²?
16. 16.Use (a + b)(a − b) = a² − b² to find 47 × 33.
17. 17.Use (a − b)² = a² − 2ab + b² to find 32².
18. 18.Use (a − b)² = a² − 2ab + b² to find 58².
19. 19.If a + b = 14 and ab = 33, what is a² + b²?
20. 20.Use (a + b)² = a² + 2ab + b² to find 74².
21. 21.Find the value of x² + 2xy + y² when x = 3 and y = 2.
22. 22.Use (a + b)(a − b) = a² − b² to find 74 × 66.
23. 23.Find the value of x² − y² when x = 5 and y = 4.
24. 24.Use (a + b)(a − b) = a² − b² to find 71 × 69.
25. 25.Use (a + b)² = a² + 2ab + b² to find 36².
26. 26.Use (a − b)² = a² − 2ab + b² to find 35².
27. 27.If a + b = 5 and ab = 6, what is a² + b²?
28. 28.If a − b = 6 and ab = 16, what is a² + b²?
29. 29.Use (a + b)² = a² + 2ab + b² to find 44².
30. 30.Use a² − b² = (a + b)(a − b) to find 93² − 67².
31. 31.Use (a + b)² = a² + 2ab + b² to find 82².
32. 32.Use (a + b)² = a² + 2ab + b² to find 37².
33. 33.Use (a − b)² = a² − 2ab + b² to find 19².
34. 34.Use a² − b² = (a + b)(a − b) to find 26² − 25².
35. 35.Find the value of x² + 2xy + y² when x = 14 and y = 5.
36. 36.Find the value of x² + 2xy + y² when x = 12 and y = 11.
37. 37.If a + b = 16 and ab = 55, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 54² − 10².
39. 39.Find the value of x² + 2xy + y² when x = 4 and y = 3.
40. 40.Use (a + b)(a − b) = a² − b² to find 24 × 16.

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