Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 227 · 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 16².
2. 2.If a + b = 4 and ab = 3, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 61² − 35².
4. 4.If a + b = 9 and ab = 18, what is a² + b²?
5. 5.Find the value of x² − 2xy + y² when x = 15 and y = 8.
6. 6.Use a² − b² = (a + b)(a − b) to find 88² − 27².
7. 7.Use (a + b)² = a² + 2ab + b² to find 23².
8. 8.Use (a + b)(a − b) = a² − b² to find 21 × 19.
9. 9.Use (a + b)(a − b) = a² − b² to find 23 × 17.
10. 10.If a − b = 1 and ab = 30, what is a² + b²?
11. 11.Find the value of x² − y² when x = 8 and y = 1.
12. 12.Find the value of x² − y² when x = 13 and y = 7.
13. 13.Use (a + b)² = a² + 2ab + b² to find 73².
14. 14.Use (a + b)² = a² + 2ab + b² to find 28².
15. 15.If a + b = 17 and ab = 60, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 72² − 42².
17. 17.Use (a + b)² = a² + 2ab + b² to find 98².
18. 18.Use (a + b)(a − b) = a² − b² to find 34 × 26.
19. 19.Use (a + b)² = a² + 2ab + b² to find 31².
20. 20.Find the value of x² − y² when x = 4 and y = 2.
21. 21.Use (a − b)² = a² − 2ab + b² to find 84².
22. 22.If a − b = 6 and ab = 55, what is a² + b²?
23. 23.Use a² − b² = (a + b)(a − b) to find 26² − 6².
24. 24.If a + b = 14 and ab = 45, what is a² + b²?
25. 25.Find the value of x² + 2xy + y² when x = 15 and y = 1.
26. 26.If a − b = 2 and ab = 15, what is a² + b²?
27. 27.If a + b = 12 and ab = 32, what is a² + b²?
28. 28.Use (a + b)² = a² + 2ab + b² to find 13².
29. 29.Use (a − b)² = a² − 2ab + b² to find 37².
30. 30.Use a² − b² = (a + b)(a − b) to find 74² − 34².
31. 31.Use (a + b)² = a² + 2ab + b² to find 37².
32. 32.Find the value of x² + 2xy + y² when x = 12 and y = 1.
33. 33.If a − b = 1 and ab = 2, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 77².
35. 35.Use (a − b)² = a² − 2ab + b² to find 17².
36. 36.Find the value of x² + 2xy + y² when x = 4 and y = 1.
37. 37.Find the value of x² − y² when x = 13 and y = 5.
38. 38.Use a² − b² = (a + b)(a − b) to find 37² − 31².
39. 39.Use (a − b)² = a² − 2ab + b² to find 64².
40. 40.Use (a + b)² = a² + 2ab + b² to find 46².

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