Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 514 · 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.Find the value of x² − y² when x = 11 and y = 6.
2. 2.Use a² − b² = (a + b)(a − b) to find 99² − 86².
3. 3.Find the value of x² − 2xy + y² when x = 11 and y = 7.
4. 4.Use (a − b)² = a² − 2ab + b² to find 73².
5. 5.Find the value of x² − 2xy + y² when x = 3 and y = 2.
6. 6.Find the value of x² + 2xy + y² when x = 6 and y = 1.
7. 7.If a + b = 14 and ab = 48, what is a² + b²?
8. 8.Use (a + b)² = a² + 2ab + b² to find 84².
9. 9.Use (a + b)(a − b) = a² − b² to find 32 × 28.
10. 10.Use (a − b)² = a² − 2ab + b² to find 86².
11. 11.Use (a + b)² = a² + 2ab + b² to find 99².
12. 12.Use (a + b)(a − b) = a² − b² to find 94 × 86.
13. 13.Use a² − b² = (a + b)(a − b) to find 54² − 1².
14. 14.Find the value of x² − y² when x = 5 and y = 1.
15. 15.Use a² − b² = (a + b)(a − b) to find 47² − 29².
16. 16.Use (a − b)² = a² − 2ab + b² to find 22².
17. 17.Use a² − b² = (a + b)(a − b) to find 37² − 27².
18. 18.Use a² − b² = (a + b)(a − b) to find 74² − 12².
19. 19.Use (a + b)(a − b) = a² − b² to find 109 × 91.
20. 20.Use (a + b)(a − b) = a² − b² to find 76 × 64.
21. 21.Find the value of x² − 2xy + y² when x = 12 and y = 5.
22. 22.Find the value of x² − 2xy + y² when x = 14 and y = 12.
23. 23.Use (a + b)² = a² + 2ab + b² to find 106².
24. 24.Use (a + b)² = a² + 2ab + b² to find 94².
25. 25.Use (a − b)² = a² − 2ab + b² to find 23².
26. 26.Use (a − b)² = a² − 2ab + b² to find 42².
27. 27.Use (a + b)² = a² + 2ab + b² to find 88².
28. 28.Use (a + b)(a − b) = a² − b² to find 36 × 24.
29. 29.Use (a + b)² = a² + 2ab + b² to find 19².
30. 30.Use (a + b)² = a² + 2ab + b² to find 23².
31. 31.Find the value of x² + 2xy + y² when x = 5 and y = 4.
32. 32.Use (a − b)² = a² − 2ab + b² to find 85².
33. 33.Use (a + b)(a − b) = a² − b² to find 31 × 29.
34. 34.Use (a + b)(a − b) = a² − b² to find 62 × 58.
35. 35.Find the value of x² − y² when x = 6 and y = 5.
36. 36.Find the value of x² − 2xy + y² when x = 8 and y = 5.
37. 37.Use (a + b)² = a² + 2ab + b² to find 54².
38. 38.Use (a − b)² = a² − 2ab + b² to find 71².
39. 39.Use a² − b² = (a + b)(a − b) to find 87² − 36².
40. 40.Use (a + b)² = a² + 2ab + b² to find 89².

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