Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 5 · 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 = 12 and y = 5.
2. 2.Find the value of x² + 2xy + y² when x = 14 and y = 6.
3. 3.Use (a − b)² = a² − 2ab + b² to find 93².
4. 4.Use (a + b)² = a² + 2ab + b² to find 105².
5. 5.Use (a + b)(a − b) = a² − b² to find 56 × 44.
6. 6.Use (a − b)² = a² − 2ab + b² to find 15².
7. 7.Find the value of x² − y² when x = 12 and y = 7.
8. 8.Use a² − b² = (a + b)(a − b) to find 75² − 34².
9. 9.Use (a + b)(a − b) = a² − b² to find 95 × 85.
10. 10.Use (a − b)² = a² − 2ab + b² to find 43².
11. 11.Use (a − b)² = a² − 2ab + b² to find 53².
12. 12.Use a² − b² = (a + b)(a − b) to find 46² − 38².
13. 13.If a + b = 7 and ab = 6, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 25 × 15.
15. 15.Use (a + b)(a − b) = a² − b² to find 102 × 98.
16. 16.If a + b = 11 and ab = 18, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 32².
18. 18.Use (a − b)² = a² − 2ab + b² to find 14².
19. 19.Find the value of x² + 2xy + y² when x = 9 and y = 6.
20. 20.Use (a + b)(a − b) = a² − b² to find 38 × 22.
21. 21.Find the value of x² − y² when x = 4 and y = 2.
22. 22.If a + b = 3 and ab = 2, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 87² − 38².
24. 24.Use (a − b)² = a² − 2ab + b² to find 16².
25. 25.Find the value of x² − 2xy + y² when x = 6 and y = 1.
26. 26.Use (a − b)² = a² − 2ab + b² to find 57².
27. 27.Find the value of x² + 2xy + y² when x = 14 and y = 2.
28. 28.If a + b = 9 and ab = 14, what is a² + b²?
29. 29.If a + b = 12 and ab = 11, what is a² + b²?
30. 30.Find the value of x² − y² when x = 7 and y = 6.
31. 31.Use (a + b)² = a² + 2ab + b² to find 93².
32. 32.Use (a + b)² = a² + 2ab + b² to find 99².
33. 33.If a − b = 2 and ab = 3, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 68².
35. 35.If a + b = 19 and ab = 90, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 97² − 35².
37. 37.Find the value of x² + 2xy + y² when x = 7 and y = 6.
38. 38.Use (a + b)(a − b) = a² − b² to find 49 × 31.
39. 39.If a + b = 15 and ab = 54, what is a² + b²?
40. 40.Use a² − b² = (a + b)(a − b) to find 98² − 18².

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