Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 308 · 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 = 11 and y = 4.
2. 2.Use (a − b)² = a² − 2ab + b² to find 81².
3. 3.Find the value of x² + 2xy + y² when x = 8 and y = 4.
4. 4.Use (a + b)² = a² + 2ab + b² to find 19².
5. 5.Use (a − b)² = a² − 2ab + b² to find 57².
6. 6.Use (a − b)² = a² − 2ab + b² to find 75².
7. 7.If a + b = 22 and ab = 120, what is a² + b²?
8. 8.Use (a − b)² = a² − 2ab + b² to find 55².
9. 9.Find the value of x² − y² when x = 8 and y = 4.
10. 10.Use (a + b)² = a² + 2ab + b² to find 108².
11. 11.Use (a + b)² = a² + 2ab + b² to find 24².
12. 12.Use (a + b)² = a² + 2ab + b² to find 28².
13. 13.Use (a + b)² = a² + 2ab + b² to find 12².
14. 14.Use a² − b² = (a + b)(a − b) to find 83² − 38².
15. 15.If a + b = 4 and ab = 3, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 42².
17. 17.Use (a + b)² = a² + 2ab + b² to find 39².
18. 18.Use (a − b)² = a² − 2ab + b² to find 48².
19. 19.Use (a + b)² = a² + 2ab + b² to find 54².
20. 20.If a + b = 7 and ab = 12, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 23 × 17.
22. 22.Use (a − b)² = a² − 2ab + b² to find 49².
23. 23.Use (a − b)² = a² − 2ab + b² to find 54².
24. 24.Use a² − b² = (a + b)(a − b) to find 39² − 31².
25. 25.If a + b = 11 and ab = 24, what is a² + b²?
26. 26.If a + b = 8 and ab = 12, what is a² + b²?
27. 27.If a + b = 3 and ab = 2, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 56².
29. 29.Use a² − b² = (a + b)(a − b) to find 61² − 21².
30. 30.Find the value of x² + 2xy + y² when x = 7 and y = 3.
31. 31.Use a² − b² = (a + b)(a − b) to find 92² − 6².
32. 32.Use a² − b² = (a + b)(a − b) to find 52² − 22².
33. 33.Use (a + b)(a − b) = a² − b² to find 39 × 21.
34. 34.Use a² − b² = (a + b)(a − b) to find 64² − 62².
35. 35.Use (a + b)(a − b) = a² − b² to find 103 × 97.
36. 36.Use (a + b)(a − b) = a² − b² to find 35 × 25.
37. 37.Find the value of x² − y² when x = 6 and y = 1.
38. 38.If a + b = 10 and ab = 24, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 90² − 13².
40. 40.If a − b = 1 and ab = 12, what is a² + b²?

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