Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 626 · 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 = 23 and ab = 132, what is a² + b²?
2. 2.If a − b = 3 and ab = 40, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 88² − 87².
4. 4.If a − b = 5 and ab = 66, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 15 and y = 3.
6. 6.Use (a + b)² = a² + 2ab + b² to find 81².
7. 7.Use a² − b² = (a + b)(a − b) to find 53² − 32².
8. 8.Use a² − b² = (a + b)(a − b) to find 34² − 20².
9. 9.Use (a − b)² = a² − 2ab + b² to find 28².
10. 10.Find the value of x² + 2xy + y² when x = 12 and y = 1.
11. 11.Find the value of x² − 2xy + y² when x = 11 and y = 10.
12. 12.Use a² − b² = (a + b)(a − b) to find 26² − 21².
13. 13.Use (a + b)(a − b) = a² − b² to find 105 × 95.
14. 14.Use (a + b)² = a² + 2ab + b² to find 25².
15. 15.Use (a − b)² = a² − 2ab + b² to find 52².
16. 16.Use (a + b)(a − b) = a² − b² to find 83 × 77.
17. 17.Use a² − b² = (a + b)(a − b) to find 30² − 3².
18. 18.Use (a − b)² = a² − 2ab + b² to find 82².
19. 19.Use (a + b)² = a² + 2ab + b² to find 13².
20. 20.Use (a + b)² = a² + 2ab + b² to find 48².
21. 21.If a − b = 3 and ab = 28, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 33².
23. 23.Use a² − b² = (a + b)(a − b) to find 34² − 30².
24. 24.Use (a − b)² = a² − 2ab + b² to find 14².
25. 25.If a − b = 2 and ab = 48, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 38 × 22.
27. 27.If a − b = 2 and ab = 3, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 76 × 64.
29. 29.Find the value of x² − 2xy + y² when x = 3 and y = 2.
30. 30.Use (a + b)² = a² + 2ab + b² to find 42².
31. 31.If a + b = 3 and ab = 2, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 63².
33. 33.If a + b = 12 and ab = 35, what is a² + b²?
34. 34.Use (a + b)² = a² + 2ab + b² to find 65².
35. 35.Use a² − b² = (a + b)(a − b) to find 55² − 51².
36. 36.Use a² − b² = (a + b)(a − b) to find 26² − 20².
37. 37.Use (a + b)(a − b) = a² − b² to find 93 × 87.
38. 38.Find the value of x² − 2xy + y² when x = 4 and y = 2.
39. 39.Use (a + b)² = a² + 2ab + b² to find 78².
40. 40.Use (a + b)(a − b) = a² − b² to find 81 × 79.

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