Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 706 · 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)² = a² − 2ab + b² to find 17².
2. 2.Use (a − b)² = a² − 2ab + b² to find 75².
3. 3.Use (a + b)(a − b) = a² − b² to find 58 × 42.
4. 4.Use (a + b)² = a² + 2ab + b² to find 46².
5. 5.Use a² − b² = (a + b)(a − b) to find 25² − 6².
6. 6.Use (a + b)² = a² + 2ab + b² to find 23².
7. 7.Use (a + b)² = a² + 2ab + b² to find 94².
8. 8.Use (a − b)² = a² − 2ab + b² to find 36².
9. 9.Use (a + b)² = a² + 2ab + b² to find 78².
10. 10.Use (a + b)(a − b) = a² − b² to find 104 × 96.
11. 11.Use a² − b² = (a + b)(a − b) to find 46² − 13².
12. 12.Use a² − b² = (a + b)(a − b) to find 47² − 43².
13. 13.Use (a − b)² = a² − 2ab + b² to find 77².
14. 14.Find the value of x² − 2xy + y² when x = 12 and y = 1.
15. 15.Find the value of x² + 2xy + y² when x = 4 and y = 3.
16. 16.If a − b = 5 and ab = 6, what is a² + b²?
17. 17.If a + b = 7 and ab = 12, what is a² + b²?
18. 18.Use a² − b² = (a + b)(a − b) to find 47² − 44².
19. 19.Use a² − b² = (a + b)(a − b) to find 73² − 1².
20. 20.Find the value of x² + 2xy + y² when x = 7 and y = 5.
21. 21.Use (a + b)² = a² + 2ab + b² to find 61².
22. 22.Use (a + b)² = a² + 2ab + b² to find 92².
23. 23.If a + b = 6 and ab = 8, what is a² + b²?
24. 24.Use (a + b)(a − b) = a² − b² to find 62 × 58.
25. 25.Use (a − b)² = a² − 2ab + b² to find 22².
26. 26.Use (a + b)(a − b) = a² − b² to find 42 × 38.
27. 27.Use (a − b)² = a² − 2ab + b² to find 48².
28. 28.Use a² − b² = (a + b)(a − b) to find 75² − 34².
29. 29.If a − b = 1 and ab = 20, what is a² + b²?
30. 30.Find the value of x² + 2xy + y² when x = 3 and y = 1.
31. 31.Use a² − b² = (a + b)(a − b) to find 79² − 34².
32. 32.Use a² − b² = (a + b)(a − b) to find 53² − 15².
33. 33.Use (a + b)(a − b) = a² − b² to find 73 × 67.
34. 34.Use (a + b)² = a² + 2ab + b² to find 18².
35. 35.If a + b = 3 and ab = 2, what is a² + b²?
36. 36.Find the value of x² − 2xy + y² when x = 7 and y = 1.
37. 37.Use (a + b)² = a² + 2ab + b² to find 51².
38. 38.Use (a + b)(a − b) = a² − b² to find 65 × 55.
39. 39.Use (a + b)² = a² + 2ab + b² to find 107².
40. 40.Use (a − b)² = a² − 2ab + b² to find 28².

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