Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 662 · 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.If a + b = 19 and ab = 84, what is a² + b²?
2. 2.Find the value of x² − 2xy + y² when x = 6 and y = 1.
3. 3.Use a² − b² = (a + b)(a − b) to find 24² − 17².
4. 4.Use (a + b)(a − b) = a² − b² to find 27 × 13.
5. 5.If a − b = 9 and ab = 36, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 106².
7. 7.Use (a − b)² = a² − 2ab + b² to find 55².
8. 8.Use (a + b)(a − b) = a² − b² to find 106 × 94.
9. 9.Use (a + b)² = a² + 2ab + b² to find 52².
10. 10.Find the value of x² + 2xy + y² when x = 9 and y = 8.
11. 11.Use a² − b² = (a + b)(a − b) to find 81² − 57².
12. 12.Use (a − b)² = a² − 2ab + b² to find 87².
13. 13.Use a² − b² = (a + b)(a − b) to find 24² − 22².
14. 14.Find the value of x² + 2xy + y² when x = 5 and y = 1.
15. 15.Use (a + b)(a − b) = a² − b² to find 33 × 27.
16. 16.Use (a + b)(a − b) = a² − b² to find 66 × 54.
17. 17.Use (a + b)² = a² + 2ab + b² to find 101².
18. 18.Use (a − b)² = a² − 2ab + b² to find 53².
19. 19.Use (a + b)(a − b) = a² − b² to find 24 × 16.
20. 20.If a − b = 2 and ab = 3, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 46 × 34.
22. 22.Use (a + b)² = a² + 2ab + b² to find 74².
23. 23.Use (a − b)² = a² − 2ab + b² to find 67².
24. 24.Use (a + b)² = a² + 2ab + b² to find 19².
25. 25.Use (a − b)² = a² − 2ab + b² to find 94².
26. 26.If a − b = 8 and ab = 9, what is a² + b²?
27. 27.Use (a + b)(a − b) = a² − b² to find 69 × 51.
28. 28.Find the value of x² − y² when x = 7 and y = 1.
29. 29.Use (a − b)² = a² − 2ab + b² to find 37².
30. 30.Use (a + b)² = a² + 2ab + b² to find 18².
31. 31.Use (a + b)² = a² + 2ab + b² to find 83².
32. 32.Use a² − b² = (a + b)(a − b) to find 82² − 71².
33. 33.If a − b = 8 and ab = 33, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 61².
35. 35.Use a² − b² = (a + b)(a − b) to find 27² − 8².
36. 36.Find the value of x² − y² when x = 4 and y = 3.
37. 37.Find the value of x² + 2xy + y² when x = 5 and y = 3.
38. 38.Use (a − b)² = a² − 2ab + b² to find 82².
39. 39.Use (a + b)² = a² + 2ab + b² to find 79².
40. 40.Find the value of x² − 2xy + y² when x = 14 and y = 13.

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