Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 450 · 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 = 6 and y = 1.
2. 2.Use (a + b)(a − b) = a² − b² to find 71 × 69.
3. 3.Use (a + b)² = a² + 2ab + b² to find 105².
4. 4.Use (a + b)² = a² + 2ab + b² to find 34².
5. 5.Use a² − b² = (a + b)(a − b) to find 72² − 13².
6. 6.Use (a + b)² = a² + 2ab + b² to find 31².
7. 7.Use a² − b² = (a + b)(a − b) to find 51² − 32².
8. 8.Use (a − b)² = a² − 2ab + b² to find 91².
9. 9.If a − b = 8 and ab = 20, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 80² − 28².
11. 11.Use a² − b² = (a + b)(a − b) to find 79² − 32².
12. 12.Find the value of x² − 2xy + y² when x = 6 and y = 3.
13. 13.If a + b = 8 and ab = 12, what is a² + b²?
14. 14.Use (a + b)(a − b) = a² − b² to find 27 × 13.
15. 15.Use (a − b)² = a² − 2ab + b² to find 67².
16. 16.If a + b = 10 and ab = 9, what is a² + b²?
17. 17.Find the value of x² − 2xy + y² when x = 6 and y = 2.
18. 18.Use (a + b)(a − b) = a² − b² to find 54 × 46.
19. 19.If a + b = 9 and ab = 20, what is a² + b²?
20. 20.Use a² − b² = (a + b)(a − b) to find 61² − 44².
21. 21.Use a² − b² = (a + b)(a − b) to find 24² − 11².
22. 22.Use (a + b)² = a² + 2ab + b² to find 39².
23. 23.Find the value of x² − 2xy + y² when x = 3 and y = 1.
24. 24.Use (a − b)² = a² − 2ab + b² to find 26².
25. 25.If a + b = 6 and ab = 5, what is a² + b²?
26. 26.Use (a + b)(a − b) = a² − b² to find 92 × 88.
27. 27.Use a² − b² = (a + b)(a − b) to find 58² − 15².
28. 28.Use a² − b² = (a + b)(a − b) to find 92² − 36².
29. 29.Use a² − b² = (a + b)(a − b) to find 65² − 19².
30. 30.If a + b = 11 and ab = 18, what is a² + b²?
31. 31.Use a² − b² = (a + b)(a − b) to find 97² − 21².
32. 32.Use (a + b)² = a² + 2ab + b² to find 37².
33. 33.Use (a + b)² = a² + 2ab + b² to find 21².
34. 34.If a + b = 16 and ab = 63, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 72 × 68.
36. 36.If a + b = 12 and ab = 35, what is a² + b²?
37. 37.Use (a + b)² = a² + 2ab + b² to find 108².
38. 38.If a + b = 3 and ab = 2, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 39².
40. 40.Find the value of x² − 2xy + y² when x = 9 and y = 8.

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