Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 306 · 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 91².
2. 2.Find the value of x² − y² when x = 8 and y = 1.
3. 3.Use a² − b² = (a + b)(a − b) to find 27² − 5².
4. 4.Use (a + b)(a − b) = a² − b² to find 42 × 38.
5. 5.Find the value of x² − y² when x = 5 and y = 2.
6. 6.Use (a − b)² = a² − 2ab + b² to find 19².
7. 7.If a − b = 5 and ab = 36, what is a² + b²?
8. 8.Use a² − b² = (a + b)(a − b) to find 86² − 75².
9. 9.Use (a + b)² = a² + 2ab + b² to find 88².
10. 10.Use (a + b)(a − b) = a² − b² to find 24 × 16.
11. 11.Find the value of x² + 2xy + y² when x = 6 and y = 2.
12. 12.Use (a + b)(a − b) = a² − b² to find 48 × 32.
13. 13.Use (a + b)² = a² + 2ab + b² to find 18².
14. 14.Use (a − b)² = a² − 2ab + b² to find 82².
15. 15.If a − b = 1 and ab = 12, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 92².
17. 17.Use (a − b)² = a² − 2ab + b² to find 96².
18. 18.Use a² − b² = (a + b)(a − b) to find 42² − 18².
19. 19.Use (a + b)² = a² + 2ab + b² to find 17².
20. 20.Use a² − b² = (a + b)(a − b) to find 84² − 44².
21. 21.Find the value of x² − y² when x = 13 and y = 3.
22. 22.Use (a + b)² = a² + 2ab + b² to find 82².
23. 23.Use (a − b)² = a² − 2ab + b² to find 85².
24. 24.Use (a − b)² = a² − 2ab + b² to find 11².
25. 25.Use a² − b² = (a + b)(a − b) to find 43² − 22².
26. 26.If a + b = 18 and ab = 72, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 28² − 26².
28. 28.Use (a − b)² = a² − 2ab + b² to find 29².
29. 29.If a − b = 3 and ab = 108, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 98².
31. 31.Use a² − b² = (a + b)(a − b) to find 22² − 11².
32. 32.Find the value of x² + 2xy + y² when x = 12 and y = 3.
33. 33.Use (a + b)² = a² + 2ab + b² to find 44².
34. 34.Find the value of x² − y² when x = 11 and y = 7.
35. 35.Find the value of x² + 2xy + y² when x = 11 and y = 6.
36. 36.Use a² − b² = (a + b)(a − b) to find 98² − 71².
37. 37.Find the value of x² − 2xy + y² when x = 9 and y = 7.
38. 38.Use a² − b² = (a + b)(a − b) to find 92² − 20².
39. 39.Use a² − b² = (a + b)(a − b) to find 90² − 55².
40. 40.Use (a + b)² = a² + 2ab + b² to find 63².

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