Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 388 · 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 = 10 and ab = 21, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 106².
3. 3.Use (a − b)² = a² − 2ab + b² to find 83².
4. 4.Use (a − b)² = a² − 2ab + b² to find 48².
5. 5.If a + b = 7 and ab = 6, what is a² + b²?
6. 6.If a + b = 12 and ab = 20, what is a² + b²?
7. 7.Use a² − b² = (a + b)(a − b) to find 29² − 18².
8. 8.Find the value of x² − 2xy + y² when x = 3 and y = 1.
9. 9.Use (a + b)² = a² + 2ab + b² to find 27².
10. 10.Use (a + b)(a − b) = a² − b² to find 96 × 84.
11. 11.If a − b = 6 and ab = 7, what is a² + b²?
12. 12.Use (a − b)² = a² − 2ab + b² to find 12².
13. 13.Use (a + b)² = a² + 2ab + b² to find 23².
14. 14.If a + b = 6 and ab = 8, what is a² + b²?
15. 15.Use (a + b)² = a² + 2ab + b² to find 91².
16. 16.Use (a − b)² = a² − 2ab + b² to find 78².
17. 17.Use (a + b)² = a² + 2ab + b² to find 55².
18. 18.Use (a + b)² = a² + 2ab + b² to find 25².
19. 19.If a + b = 11 and ab = 30, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 58² − 18².
21. 21.Use (a + b)² = a² + 2ab + b² to find 81².
22. 22.Use (a + b)(a − b) = a² − b² to find 49 × 31.
23. 23.Use (a − b)² = a² − 2ab + b² to find 13².
24. 24.Use a² − b² = (a + b)(a − b) to find 35² − 5².
25. 25.Use (a − b)² = a² − 2ab + b² to find 81².
26. 26.Use a² − b² = (a + b)(a − b) to find 24² − 20².
27. 27.Find the value of x² − 2xy + y² when x = 11 and y = 6.
28. 28.Use (a + b)(a − b) = a² − b² to find 64 × 56.
29. 29.Use (a + b)(a − b) = a² − b² to find 34 × 26.
30. 30.Find the value of x² − y² when x = 4 and y = 1.
31. 31.Use a² − b² = (a + b)(a − b) to find 52² − 35².
32. 32.Use (a + b)² = a² + 2ab + b² to find 13².
33. 33.Use (a + b)² = a² + 2ab + b² to find 73².
34. 34.Find the value of x² + 2xy + y² when x = 7 and y = 5.
35. 35.Use (a + b)² = a² + 2ab + b² to find 107².
36. 36.Use (a + b)(a − b) = a² − b² to find 61 × 59.
37. 37.Use (a − b)² = a² − 2ab + b² to find 25².
38. 38.Use (a + b)² = a² + 2ab + b² to find 33².
39. 39.Use (a + b)(a − b) = a² − b² to find 75 × 65.
40. 40.Use (a + b)(a − b) = a² − b² to find 33 × 27.

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