Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 941 · 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 25 × 15.
2. 2.Use (a + b)² = a² + 2ab + b² to find 47².
3. 3.If a − b = 1 and ab = 2, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 76².
5. 5.Use (a + b)² = a² + 2ab + b² to find 49².
6. 6.Use (a + b)² = a² + 2ab + b² to find 24².
7. 7.Use (a + b)² = a² + 2ab + b² to find 39².
8. 8.Use (a + b)² = a² + 2ab + b² to find 19².
9. 9.Use (a + b)² = a² + 2ab + b² to find 61².
10. 10.Find the value of x² − y² when x = 12 and y = 5.
11. 11.Use (a + b)(a − b) = a² − b² to find 42 × 38.
12. 12.Use (a + b)² = a² + 2ab + b² to find 11².
13. 13.Use (a + b)(a − b) = a² − b² to find 49 × 31.
14. 14.Use (a − b)² = a² − 2ab + b² to find 97².
15. 15.If a + b = 17 and ab = 60, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 31².
17. 17.Find the value of x² + 2xy + y² when x = 6 and y = 5.
18. 18.Use a² − b² = (a + b)(a − b) to find 52² − 44².
19. 19.Use (a + b)(a − b) = a² − b² to find 36 × 24.
20. 20.Use (a + b)(a − b) = a² − b² to find 104 × 96.
21. 21.Use (a + b)² = a² + 2ab + b² to find 107².
22. 22.Use a² − b² = (a + b)(a − b) to find 63² − 44².
23. 23.Use (a − b)² = a² − 2ab + b² to find 15².
24. 24.Use (a − b)² = a² − 2ab + b² to find 66².
25. 25.Use (a + b)² = a² + 2ab + b² to find 44².
26. 26.Use (a + b)² = a² + 2ab + b² to find 88².
27. 27.If a + b = 11 and ab = 30, what is a² + b²?
28. 28.Use a² − b² = (a + b)(a − b) to find 77² − 42².
29. 29.Use (a + b)² = a² + 2ab + b² to find 92².
30. 30.Find the value of x² − y² when x = 3 and y = 1.
31. 31.If a + b = 5 and ab = 6, what is a² + b²?
32. 32.Find the value of x² − y² when x = 12 and y = 8.
33. 33.Use (a − b)² = a² − 2ab + b² to find 28².
34. 34.If a + b = 15 and ab = 36, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 84².
36. 36.Find the value of x² − y² when x = 5 and y = 3.
37. 37.If a − b = 4 and ab = 12, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 92² − 68².
39. 39.Use (a + b)² = a² + 2ab + b² to find 16².
40. 40.Use (a + b)(a − b) = a² − b² to find 23 × 17.

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