Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 622 · 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.If a + b = 3 and ab = 2, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 38².
3. 3.Find the value of x² − 2xy + y² when x = 12 and y = 8.
4. 4.Use (a − b)² = a² − 2ab + b² to find 29².
5. 5.Use (a + b)² = a² + 2ab + b² to find 11².
6. 6.Find the value of x² − 2xy + y² when x = 3 and y = 1.
7. 7.Use a² − b² = (a + b)(a − b) to find 70² − 56².
8. 8.Use (a + b)² = a² + 2ab + b² to find 28².
9. 9.If a + b = 18 and ab = 77, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 96² − 53².
11. 11.Find the value of x² + 2xy + y² when x = 14 and y = 3.
12. 12.Use a² − b² = (a + b)(a − b) to find 72² − 69².
13. 13.Use (a + b)² = a² + 2ab + b² to find 13².
14. 14.Use (a + b)(a − b) = a² − b² to find 41 × 39.
15. 15.Use (a + b)² = a² + 2ab + b² to find 84².
16. 16.Use (a + b)² = a² + 2ab + b² to find 101².
17. 17.Find the value of x² − y² when x = 15 and y = 7.
18. 18.Use (a + b)² = a² + 2ab + b² to find 61².
19. 19.If a + b = 7 and ab = 12, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 31² − 30².
21. 21.Use (a − b)² = a² − 2ab + b² to find 64².
22. 22.If a − b = 3 and ab = 10, what is a² + b²?
23. 23.Use (a − b)² = a² − 2ab + b² to find 14².
24. 24.Find the value of x² − 2xy + y² when x = 4 and y = 1.
25. 25.Use a² − b² = (a + b)(a − b) to find 52² − 42².
26. 26.Use (a + b)² = a² + 2ab + b² to find 99².
27. 27.Find the value of x² − y² when x = 4 and y = 2.
28. 28.Use a² − b² = (a + b)(a − b) to find 89² − 49².
29. 29.If a + b = 5 and ab = 6, what is a² + b²?
30. 30.Find the value of x² + 2xy + y² when x = 14 and y = 12.
31. 31.Find the value of x² − 2xy + y² when x = 6 and y = 3.
32. 32.Find the value of x² − y² when x = 7 and y = 1.
33. 33.Use a² − b² = (a + b)(a − b) to find 20² − 9².
34. 34.Find the value of x² − y² when x = 4 and y = 3.
35. 35.Use (a − b)² = a² − 2ab + b² to find 16².
36. 36.Use (a + b)(a − b) = a² − b² to find 24 × 16.
37. 37.Find the value of x² − y² when x = 6 and y = 4.
38. 38.Use (a − b)² = a² − 2ab + b² to find 39².
39. 39.If a + b = 8 and ab = 15, what is a² + b²?
40. 40.Find the value of x² + 2xy + y² when x = 12 and y = 5.

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