Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 341 · 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 = 14 and ab = 24, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 42².
3. 3.Use (a − b)² = a² − 2ab + b² to find 61².
4. 4.Find the value of x² − y² when x = 6 and y = 2.
5. 5.If a + b = 7 and ab = 6, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 89 × 71.
7. 7.Use a² − b² = (a + b)(a − b) to find 39² − 14².
8. 8.Use a² − b² = (a + b)(a − b) to find 31² − 30².
9. 9.Use (a − b)² = a² − 2ab + b² to find 12².
10. 10.Use (a + b)(a − b) = a² − b² to find 66 × 54.
11. 11.If a + b = 7 and ab = 10, what is a² + b²?
12. 12.If a + b = 13 and ab = 40, what is a² + b²?
13. 13.Find the value of x² − y² when x = 7 and y = 6.
14. 14.Use a² − b² = (a + b)(a − b) to find 21² − 20².
15. 15.Use (a + b)² = a² + 2ab + b² to find 16².
16. 16.Find the value of x² + 2xy + y² when x = 13 and y = 7.
17. 17.If a − b = 5 and ab = 6, what is a² + b²?
18. 18.Find the value of x² − 2xy + y² when x = 3 and y = 1.
19. 19.Use (a + b)² = a² + 2ab + b² to find 31².
20. 20.If a − b = 2 and ab = 8, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 75².
22. 22.Use a² − b² = (a + b)(a − b) to find 99² − 29².
23. 23.Use a² − b² = (a + b)(a − b) to find 30² − 11².
24. 24.Use (a + b)² = a² + 2ab + b² to find 102².
25. 25.Use (a − b)² = a² − 2ab + b² to find 92².
26. 26.Use (a − b)² = a² − 2ab + b² to find 51².
27. 27.Use a² − b² = (a + b)(a − b) to find 66² − 54².
28. 28.Use (a + b)(a − b) = a² − b² to find 79 × 61.
29. 29.Use (a − b)² = a² − 2ab + b² to find 14².
30. 30.If a − b = 3 and ab = 70, what is a² + b²?
31. 31.Use (a + b)² = a² + 2ab + b² to find 76².
32. 32.If a + b = 11 and ab = 28, what is a² + b²?
33. 33.Find the value of x² − 2xy + y² when x = 9 and y = 4.
34. 34.Use (a + b)² = a² + 2ab + b² to find 61².
35. 35.Use a² − b² = (a + b)(a − b) to find 22² − 6².
36. 36.Use (a + b)(a − b) = a² − b² to find 68 × 52.
37. 37.Use (a + b)² = a² + 2ab + b² to find 65².
38. 38.Find the value of x² − y² when x = 13 and y = 1.
39. 39.Find the value of x² − y² when x = 14 and y = 9.
40. 40.Use (a − b)² = a² − 2ab + b² to find 89².

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