Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 993 · 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 = 15 and y = 7.
2. 2.If a − b = 5 and ab = 24, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 84² − 57².
4. 4.Use (a − b)² = a² − 2ab + b² to find 95².
5. 5.Use (a + b)² = a² + 2ab + b² to find 37².
6. 6.Use (a − b)² = a² − 2ab + b² to find 48².
7. 7.Use (a + b)² = a² + 2ab + b² to find 103².
8. 8.Use a² − b² = (a + b)(a − b) to find 56² − 37².
9. 9.Use (a + b)² = a² + 2ab + b² to find 102².
10. 10.If a − b = 1 and ab = 110, what is a² + b²?
11. 11.Find the value of x² − y² when x = 13 and y = 3.
12. 12.If a + b = 16 and ab = 55, what is a² + b²?
13. 13.Use (a − b)² = a² − 2ab + b² to find 35².
14. 14.Use (a + b)(a − b) = a² − b² to find 79 × 61.
15. 15.Use (a + b)(a − b) = a² − b² to find 24 × 16.
16. 16.Use (a − b)² = a² − 2ab + b² to find 93².
17. 17.Find the value of x² − y² when x = 3 and y = 2.
18. 18.Use (a + b)² = a² + 2ab + b² to find 89².
19. 19.Use (a − b)² = a² − 2ab + b² to find 38².
20. 20.If a + b = 15 and ab = 50, what is a² + b²?
21. 21.If a − b = 6 and ab = 27, what is a² + b²?
22. 22.Find the value of x² − 2xy + y² when x = 9 and y = 5.
23. 23.If a − b = 4 and ab = 60, what is a² + b²?
24. 24.Find the value of x² + 2xy + y² when x = 5 and y = 1.
25. 25.Use a² − b² = (a + b)(a − b) to find 25² − 23².
26. 26.Use (a + b)(a − b) = a² − b² to find 68 × 52.
27. 27.Use (a + b)² = a² + 2ab + b² to find 73².
28. 28.Use (a − b)² = a² − 2ab + b² to find 31².
29. 29.If a + b = 17 and ab = 66, what is a² + b²?
30. 30.Find the value of x² − 2xy + y² when x = 5 and y = 1.
31. 31.Use (a + b)² = a² + 2ab + b² to find 51².
32. 32.If a + b = 5 and ab = 4, what is a² + b²?
33. 33.Use (a + b)(a − b) = a² − b² to find 94 × 86.
34. 34.Use (a + b)(a − b) = a² − b² to find 31 × 29.
35. 35.If a − b = 3 and ab = 28, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 34².
37. 37.If a + b = 12 and ab = 35, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 87².
39. 39.Use (a − b)² = a² − 2ab + b² to find 34².
40. 40.Use a² − b² = (a + b)(a − b) to find 92² − 85².

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