Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 783 · 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)(a − b) = a² − b² to find 108 × 92.
2. 2.Find the value of x² + 2xy + y² when x = 9 and y = 4.
3. 3.Find the value of x² − y² when x = 10 and y = 4.
4. 4.Use (a − b)² = a² − 2ab + b² to find 27².
5. 5.Use a² − b² = (a + b)(a − b) to find 87² − 49².
6. 6.Use (a − b)² = a² − 2ab + b² to find 34².
7. 7.Use a² − b² = (a + b)(a − b) to find 35² − 2².
8. 8.Use (a − b)² = a² − 2ab + b² to find 52².
9. 9.If a + b = 12 and ab = 27, what is a² + b²?
10. 10.If a − b = 2 and ab = 80, what is a² + b²?
11. 11.Use (a + b)(a − b) = a² − b² to find 76 × 64.
12. 12.Use a² − b² = (a + b)(a − b) to find 24² − 11².
13. 13.Use (a + b)² = a² + 2ab + b² to find 21².
14. 14.Use (a + b)(a − b) = a² − b² to find 68 × 52.
15. 15.Find the value of x² − y² when x = 13 and y = 8.
16. 16.Use (a + b)(a − b) = a² − b² to find 109 × 91.
17. 17.Use a² − b² = (a + b)(a − b) to find 42² − 16².
18. 18.If a − b = 3 and ab = 28, what is a² + b²?
19. 19.Use (a + b)² = a² + 2ab + b² to find 75².
20. 20.Use (a + b)(a − b) = a² − b² to find 26 × 14.
21. 21.Use a² − b² = (a + b)(a − b) to find 35² − 29².
22. 22.Use a² − b² = (a + b)(a − b) to find 39² − 25².
23. 23.Use (a − b)² = a² − 2ab + b² to find 17².
24. 24.Use (a − b)² = a² − 2ab + b² to find 88².
25. 25.Use a² − b² = (a + b)(a − b) to find 35² − 9².
26. 26.Use (a + b)(a − b) = a² − b² to find 53 × 47.
27. 27.If a + b = 9 and ab = 8, what is a² + b²?
28. 28.Use (a − b)² = a² − 2ab + b² to find 62².
29. 29.Use (a − b)² = a² − 2ab + b² to find 38².
30. 30.Use (a + b)(a − b) = a² − b² to find 77 × 63.
31. 31.Use (a + b)(a − b) = a² − b² to find 89 × 71.
32. 32.If a + b = 14 and ab = 45, what is a² + b²?
33. 33.Use (a + b)² = a² + 2ab + b² to find 87².
34. 34.If a + b = 5 and ab = 4, what is a² + b²?
35. 35.If a + b = 4 and ab = 3, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 46².
37. 37.Find the value of x² − y² when x = 6 and y = 1.
38. 38.Use (a + b)(a − b) = a² − b² to find 52 × 48.
39. 39.Find the value of x² − y² when x = 6 and y = 2.
40. 40.Use (a + b)² = a² + 2ab + b² to find 32².

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