Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 162 · 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 + 2xy + y² when x = 5 and y = 3.
2. 2.Use a² − b² = (a + b)(a − b) to find 99² − 19².
3. 3.If a − b = 3 and ab = 18, what is a² + b²?
4. 4.Use (a − b)² = a² − 2ab + b² to find 97².
5. 5.Find the value of x² + 2xy + y² when x = 5 and y = 1.
6. 6.Use (a − b)² = a² − 2ab + b² to find 22².
7. 7.Use a² − b² = (a + b)(a − b) to find 56² − 34².
8. 8.Use (a − b)² = a² − 2ab + b² to find 36².
9. 9.Use (a + b)² = a² + 2ab + b² to find 41².
10. 10.Use (a + b)(a − b) = a² − b² to find 82 × 78.
11. 11.If a + b = 8 and ab = 12, what is a² + b²?
12. 12.If a − b = 2 and ab = 15, what is a² + b²?
13. 13.If a + b = 8 and ab = 7, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 104².
15. 15.Use (a + b)² = a² + 2ab + b² to find 105².
16. 16.Use (a + b)(a − b) = a² − b² to find 105 × 95.
17. 17.If a + b = 8 and ab = 15, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 24² − 9².
19. 19.Use (a + b)² = a² + 2ab + b² to find 76².
20. 20.Use a² − b² = (a + b)(a − b) to find 83² − 54².
21. 21.If a + b = 12 and ab = 11, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 79².
23. 23.Use (a + b)(a − b) = a² − b² to find 28 × 12.
24. 24.Use (a − b)² = a² − 2ab + b² to find 94².
25. 25.If a + b = 3 and ab = 2, what is a² + b²?
26. 26.Find the value of x² − 2xy + y² when x = 10 and y = 3.
27. 27.If a + b = 13 and ab = 22, what is a² + b²?
28. 28.Find the value of x² − y² when x = 14 and y = 11.
29. 29.Use (a + b)(a − b) = a² − b² to find 72 × 68.
30. 30.Use (a − b)² = a² − 2ab + b² to find 17².
31. 31.Use (a − b)² = a² − 2ab + b² to find 84².
32. 32.If a − b = 4 and ab = 45, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 93 × 87.
34. 34.Find the value of x² + 2xy + y² when x = 3 and y = 1.
35. 35.Use a² − b² = (a + b)(a − b) to find 29² − 11².
36. 36.Find the value of x² + 2xy + y² when x = 14 and y = 11.
37. 37.Find the value of x² − 2xy + y² when x = 4 and y = 3.
38. 38.If a − b = 6 and ab = 72, what is a² + b²?
39. 39.Find the value of x² + 2xy + y² when x = 4 and y = 1.
40. 40.Use (a + b)(a − b) = a² − b² to find 83 × 77.

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