Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 490 · 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.Find the value of x² − y² when x = 9 and y = 2.
2. 2.Find the value of x² − y² when x = 3 and y = 2.
3. 3.Find the value of x² − y² when x = 5 and y = 3.
4. 4.Find the value of x² + 2xy + y² when x = 13 and y = 2.
5. 5.Find the value of x² − y² when x = 6 and y = 5.
6. 6.Use (a + b)² = a² + 2ab + b² to find 37².
7. 7.Find the value of x² − y² when x = 7 and y = 4.
8. 8.Use (a − b)² = a² − 2ab + b² to find 41².
9. 9.Use (a + b)² = a² + 2ab + b² to find 81².
10. 10.If a − b = 1 and ab = 6, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 107 × 93.
12. 12.Find the value of x² − y² when x = 14 and y = 13.
13. 13.Use (a + b)² = a² + 2ab + b² to find 62².
14. 14.Use (a − b)² = a² − 2ab + b² to find 17².
15. 15.Use (a + b)(a − b) = a² − b² to find 62 × 58.
16. 16.Find the value of x² + 2xy + y² when x = 12 and y = 1.
17. 17.Find the value of x² + 2xy + y² when x = 5 and y = 1.
18. 18.If a + b = 12 and ab = 35, what is a² + b²?
19. 19.Find the value of x² − y² when x = 11 and y = 9.
20. 20.Use (a + b)(a − b) = a² − b² to find 35 × 25.
21. 21.Use (a + b)(a − b) = a² − b² to find 68 × 52.
22. 22.Use (a + b)² = a² + 2ab + b² to find 71².
23. 23.Use a² − b² = (a + b)(a − b) to find 61² − 5².
24. 24.If a + b = 5 and ab = 6, what is a² + b²?
25. 25.Use (a − b)² = a² − 2ab + b² to find 73².
26. 26.Use (a + b)² = a² + 2ab + b² to find 99².
27. 27.Use (a + b)² = a² + 2ab + b² to find 34².
28. 28.Use (a + b)(a − b) = a² − b² to find 33 × 27.
29. 29.Use (a + b)(a − b) = a² − b² to find 59 × 41.
30. 30.Use a² − b² = (a + b)(a − b) to find 65² − 38².
31. 31.Find the value of x² − y² when x = 13 and y = 2.
32. 32.Use (a + b)² = a² + 2ab + b² to find 54².
33. 33.If a − b = 2 and ab = 120, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 98 × 82.
35. 35.Use (a + b)(a − b) = a² − b² to find 58 × 42.
36. 36.If a − b = 1 and ab = 20, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 96².
38. 38.Use a² − b² = (a + b)(a − b) to find 81² − 56².
39. 39.Find the value of x² + 2xy + y² when x = 4 and y = 1.
40. 40.Find the value of x² + 2xy + y² when x = 7 and y = 2.

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