Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 890 · 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 77².
2. 2.Use (a + b)² = a² + 2ab + b² to find 63².
3. 3.Use a² − b² = (a + b)(a − b) to find 89² − 79².
4. 4.Use (a − b)² = a² − 2ab + b² to find 89².
5. 5.Use a² − b² = (a + b)(a − b) to find 65² − 33².
6. 6.Use a² − b² = (a + b)(a − b) to find 67² − 26².
7. 7.Use (a − b)² = a² − 2ab + b² to find 59².
8. 8.If a − b = 10 and ab = 11, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 22² − 10².
10. 10.Use (a + b)² = a² + 2ab + b² to find 17².
11. 11.Use a² − b² = (a + b)(a − b) to find 62² − 46².
12. 12.If a + b = 5 and ab = 6, what is a² + b²?
13. 13.If a + b = 11 and ab = 30, what is a² + b²?
14. 14.Use (a + b)² = a² + 2ab + b² to find 108².
15. 15.Use (a + b)(a − b) = a² − b² to find 105 × 95.
16. 16.If a + b = 3 and ab = 2, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 96² − 51².
18. 18.Find the value of x² + 2xy + y² when x = 11 and y = 4.
19. 19.Use (a + b)² = a² + 2ab + b² to find 43².
20. 20.Use (a − b)² = a² − 2ab + b² to find 43².
21. 21.Use (a + b)(a − b) = a² − b² to find 72 × 68.
22. 22.Use (a + b)² = a² + 2ab + b² to find 34².
23. 23.Find the value of x² − 2xy + y² when x = 7 and y = 6.
24. 24.Use (a − b)² = a² − 2ab + b² to find 31².
25. 25.Use a² − b² = (a + b)(a − b) to find 99² − 33².
26. 26.Find the value of x² − 2xy + y² when x = 3 and y = 1.
27. 27.Use (a − b)² = a² − 2ab + b² to find 26².
28. 28.Use (a − b)² = a² − 2ab + b² to find 84².
29. 29.Use (a + b)² = a² + 2ab + b² to find 65².
30. 30.Use (a + b)(a − b) = a² − b² to find 44 × 36.
31. 31.Use (a − b)² = a² − 2ab + b² to find 35².
32. 32.Find the value of x² − 2xy + y² when x = 14 and y = 12.
33. 33.If a + b = 8 and ab = 12, what is a² + b²?
34. 34.Find the value of x² − 2xy + y² when x = 13 and y = 6.
35. 35.Use (a − b)² = a² − 2ab + b² to find 83².
36. 36.Use a² − b² = (a + b)(a − b) to find 47² − 16².
37. 37.Use (a + b)² = a² + 2ab + b² to find 57².
38. 38.Find the value of x² − 2xy + y² when x = 13 and y = 9.
39. 39.If a + b = 20 and ab = 96, what is a² + b²?
40. 40.If a + b = 21 and ab = 110, what is a² + b²?

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