Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 381 · 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 = 12 and y = 2.
2. 2.Use (a + b)² = a² + 2ab + b² to find 66².
3. 3.Use a² − b² = (a + b)(a − b) to find 21² − 11².
4. 4.Use (a + b)(a − b) = a² − b² to find 51 × 49.
5. 5.If a + b = 3 and ab = 2, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 105².
7. 7.If a − b = 6 and ab = 55, what is a² + b²?
8. 8.Find the value of x² + 2xy + y² when x = 7 and y = 3.
9. 9.Find the value of x² + 2xy + y² when x = 3 and y = 1.
10. 10.Use a² − b² = (a + b)(a − b) to find 43² − 12².
11. 11.If a − b = 1 and ab = 30, what is a² + b²?
12. 12.Find the value of x² + 2xy + y² when x = 14 and y = 3.
13. 13.If a + b = 6 and ab = 8, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 77² − 14².
15. 15.Use a² − b² = (a + b)(a − b) to find 90² − 80².
16. 16.Use (a − b)² = a² − 2ab + b² to find 47².
17. 17.Use a² − b² = (a + b)(a − b) to find 43² − 23².
18. 18.Use (a + b)(a − b) = a² − b² to find 53 × 47.
19. 19.Use (a − b)² = a² − 2ab + b² to find 55².
20. 20.Use (a − b)² = a² − 2ab + b² to find 91².
21. 21.If a − b = 2 and ab = 3, what is a² + b²?
22. 22.Find the value of x² − y² when x = 11 and y = 3.
23. 23.Use (a + b)(a − b) = a² − b² to find 105 × 95.
24. 24.Use (a + b)² = a² + 2ab + b² to find 58².
25. 25.Use (a + b)² = a² + 2ab + b² to find 37².
26. 26.Find the value of x² − 2xy + y² when x = 7 and y = 5.
27. 27.Find the value of x² + 2xy + y² when x = 6 and y = 4.
28. 28.Use (a + b)² = a² + 2ab + b² to find 11².
29. 29.Use (a + b)² = a² + 2ab + b² to find 44².
30. 30.If a − b = 2 and ab = 15, what is a² + b²?
31. 31.Use (a − b)² = a² − 2ab + b² to find 52².
32. 32.If a + b = 12 and ab = 32, what is a² + b²?
33. 33.Find the value of x² + 2xy + y² when x = 7 and y = 6.
34. 34.Use (a − b)² = a² − 2ab + b² to find 24².
35. 35.Use (a + b)(a − b) = a² − b² to find 49 × 31.
36. 36.Use (a + b)(a − b) = a² − b² to find 47 × 33.
37. 37.Use (a + b)² = a² + 2ab + b² to find 72².
38. 38.Use (a − b)² = a² − 2ab + b² to find 39².
39. 39.Use a² − b² = (a + b)(a − b) to find 42² − 6².
40. 40.Use (a + b)² = a² + 2ab + b² to find 97².

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