Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 633 · 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.If a + b = 15 and ab = 36, what is a² + b²?
2. 2.Use (a − b)² = a² − 2ab + b² to find 75².
3. 3.Find the value of x² − y² when x = 10 and y = 1.
4. 4.Use (a − b)² = a² − 2ab + b² to find 35².
5. 5.Find the value of x² + 2xy + y² when x = 14 and y = 13.
6. 6.Use a² − b² = (a + b)(a − b) to find 98² − 43².
7. 7.Use a² − b² = (a + b)(a − b) to find 88² − 17².
8. 8.Find the value of x² − y² when x = 10 and y = 9.
9. 9.If a + b = 6 and ab = 5, what is a² + b²?
10. 10.Use a² − b² = (a + b)(a − b) to find 42² − 16².
11. 11.Use (a + b)(a − b) = a² − b² to find 49 × 31.
12. 12.Find the value of x² + 2xy + y² when x = 13 and y = 11.
13. 13.Use (a + b)(a − b) = a² − b² to find 98 × 82.
14. 14.Use (a + b)(a − b) = a² − b² to find 41 × 39.
15. 15.Find the value of x² − 2xy + y² when x = 4 and y = 2.
16. 16.Use (a + b)² = a² + 2ab + b² to find 33².
17. 17.Find the value of x² + 2xy + y² when x = 15 and y = 1.
18. 18.Use (a − b)² = a² − 2ab + b² to find 16².
19. 19.Find the value of x² − y² when x = 5 and y = 3.
20. 20.Use (a + b)(a − b) = a² − b² to find 42 × 38.
21. 21.Use (a + b)² = a² + 2ab + b² to find 108².
22. 22.Use a² − b² = (a + b)(a − b) to find 96² − 10².
23. 23.If a − b = 5 and ab = 36, what is a² + b²?
24. 24.Use a² − b² = (a + b)(a − b) to find 94² − 11².
25. 25.Use (a + b)(a − b) = a² − b² to find 95 × 85.
26. 26.Use (a + b)² = a² + 2ab + b² to find 37².
27. 27.Use (a + b)² = a² + 2ab + b² to find 15².
28. 28.Use (a + b)² = a² + 2ab + b² to find 35².
29. 29.Use (a − b)² = a² − 2ab + b² to find 34².
30. 30.Use a² − b² = (a + b)(a − b) to find 93² − 55².
31. 31.Use (a + b)² = a² + 2ab + b² to find 82².
32. 32.Use (a − b)² = a² − 2ab + b² to find 53².
33. 33.Use (a + b)(a − b) = a² − b² to find 34 × 26.
34. 34.If a − b = 2 and ab = 8, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 71 × 69.
36. 36.Use (a − b)² = a² − 2ab + b² to find 61².
37. 37.If a − b = 8 and ab = 20, what is a² + b²?
38. 38.Use (a − b)² = a² − 2ab + b² to find 82².
39. 39.Use a² − b² = (a + b)(a − b) to find 29² − 9².
40. 40.Use (a − b)² = a² − 2ab + b² to find 28².

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