Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 830 · 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.Use (a + b)(a − b) = a² − b² to find 72 × 68.
2. 2.Use (a + b)(a − b) = a² − b² to find 41 × 39.
3. 3.If a + b = 4 and ab = 3, what is a² + b²?
4. 4.Use a² − b² = (a + b)(a − b) to find 42² − 13².
5. 5.Use (a + b)² = a² + 2ab + b² to find 73².
6. 6.Find the value of x² − 2xy + y² when x = 14 and y = 7.
7. 7.Use a² − b² = (a + b)(a − b) to find 60² − 1².
8. 8.Find the value of x² + 2xy + y² when x = 10 and y = 8.
9. 9.Use (a − b)² = a² − 2ab + b² to find 41².
10. 10.Use (a + b)² = a² + 2ab + b² to find 107².
11. 11.Use (a + b)(a − b) = a² − b² to find 87 × 73.
12. 12.Use a² − b² = (a + b)(a − b) to find 94² − 70².
13. 13.Find the value of x² + 2xy + y² when x = 14 and y = 8.
14. 14.Use a² − b² = (a + b)(a − b) to find 30² − 27².
15. 15.Find the value of x² + 2xy + y² when x = 11 and y = 10.
16. 16.Use (a + b)² = a² + 2ab + b² to find 88².
17. 17.Find the value of x² − 2xy + y² when x = 15 and y = 4.
18. 18.Use (a + b)(a − b) = a² − b² to find 32 × 28.
19. 19.Use a² − b² = (a + b)(a − b) to find 53² − 20².
20. 20.Use a² − b² = (a + b)(a − b) to find 47² − 24².
21. 21.Find the value of x² − y² when x = 6 and y = 1.
22. 22.Use a² − b² = (a + b)(a − b) to find 38² − 27².
23. 23.Use (a − b)² = a² − 2ab + b² to find 85².
24. 24.Use (a − b)² = a² − 2ab + b² to find 26².
25. 25.Use (a − b)² = a² − 2ab + b² to find 93².
26. 26.Find the value of x² − 2xy + y² when x = 4 and y = 2.
27. 27.Use (a + b)(a − b) = a² − b² to find 105 × 95.
28. 28.Use (a + b)(a − b) = a² − b² to find 26 × 14.
29. 29.Use (a + b)(a − b) = a² − b² to find 37 × 23.
30. 30.Find the value of x² − 2xy + y² when x = 6 and y = 2.
31. 31.Use (a − b)² = a² − 2ab + b² to find 87².
32. 32.Use (a + b)² = a² + 2ab + b² to find 37².
33. 33.Use (a − b)² = a² − 2ab + b² to find 29².
34. 34.Use (a − b)² = a² − 2ab + b² to find 55².
35. 35.If a + b = 13 and ab = 40, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 86².
37. 37.Use a² − b² = (a + b)(a − b) to find 67² − 31².
38. 38.Use a² − b² = (a + b)(a − b) to find 31² − 9².
39. 39.Find the value of x² − 2xy + y² when x = 5 and y = 3.
40. 40.Use a² − b² = (a + b)(a − b) to find 25² − 4².

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