Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 924 · 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 a² − b² = (a + b)(a − b) to find 53² − 47².
2. 2.Use (a − b)² = a² − 2ab + b² to find 31².
3. 3.Use (a − b)² = a² − 2ab + b² to find 55².
4. 4.Find the value of x² − y² when x = 3 and y = 1.
5. 5.If a + b = 5 and ab = 6, what is a² + b²?
6. 6.Use a² − b² = (a + b)(a − b) to find 83² − 11².
7. 7.Use (a + b)(a − b) = a² − b² to find 22 × 18.
8. 8.Use a² − b² = (a + b)(a − b) to find 43² − 13².
9. 9.Use (a + b)² = a² + 2ab + b² to find 31².
10. 10.Use a² − b² = (a + b)(a − b) to find 67² − 34².
11. 11.Use (a + b)(a − b) = a² − b² to find 35 × 25.
12. 12.Use (a + b)² = a² + 2ab + b² to find 24².
13. 13.Use a² − b² = (a + b)(a − b) to find 42² − 11².
14. 14.Find the value of x² − 2xy + y² when x = 4 and y = 1.
15. 15.Use (a − b)² = a² − 2ab + b² to find 68².
16. 16.Use (a + b)² = a² + 2ab + b² to find 11².
17. 17.Use (a − b)² = a² − 2ab + b² to find 36².
18. 18.Use (a + b)² = a² + 2ab + b² to find 32².
19. 19.Find the value of x² + 2xy + y² when x = 6 and y = 2.
20. 20.Use (a − b)² = a² − 2ab + b² to find 21².
21. 21.If a + b = 4 and ab = 3, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 23 × 17.
23. 23.Use (a + b)(a − b) = a² − b² to find 62 × 58.
24. 24.Find the value of x² + 2xy + y² when x = 13 and y = 9.
25. 25.If a + b = 22 and ab = 120, what is a² + b²?
26. 26.Use a² − b² = (a + b)(a − b) to find 27² − 2².
27. 27.Use (a + b)² = a² + 2ab + b² to find 74².
28. 28.Use a² − b² = (a + b)(a − b) to find 66² − 16².
29. 29.Use (a − b)² = a² − 2ab + b² to find 37².
30. 30.Find the value of x² − 2xy + y² when x = 10 and y = 1.
31. 31.Find the value of x² − 2xy + y² when x = 9 and y = 7.
32. 32.If a + b = 16 and ab = 63, what is a² + b²?
33. 33.Use (a − b)² = a² − 2ab + b² to find 79².
34. 34.Find the value of x² − 2xy + y² when x = 7 and y = 6.
35. 35.Use (a + b)(a − b) = a² − b² to find 108 × 92.
36. 36.Use a² − b² = (a + b)(a − b) to find 83² − 9².
37. 37.Use (a + b)(a − b) = a² − b² to find 54 × 46.
38. 38.Use (a + b)² = a² + 2ab + b² to find 68².
39. 39.Find the value of x² − 2xy + y² when x = 8 and y = 1.
40. 40.Find the value of x² + 2xy + y² when x = 7 and y = 3.

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