Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 858 · 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 48².
2. 2.Use a² − b² = (a + b)(a − b) to find 79² − 27².
3. 3.Use (a − b)² = a² − 2ab + b² to find 75².
4. 4.Use (a − b)² = a² − 2ab + b² to find 61².
5. 5.Use (a + b)² = a² + 2ab + b² to find 102².
6. 6.Use a² − b² = (a + b)(a − b) to find 38² − 19².
7. 7.Use (a − b)² = a² − 2ab + b² to find 34².
8. 8.Use (a + b)² = a² + 2ab + b² to find 67².
9. 9.Use a² − b² = (a + b)(a − b) to find 42² − 36².
10. 10.Use (a + b)² = a² + 2ab + b² to find 35².
11. 11.Find the value of x² + 2xy + y² when x = 10 and y = 7.
12. 12.Find the value of x² + 2xy + y² when x = 4 and y = 1.
13. 13.Find the value of x² − y² when x = 3 and y = 1.
14. 14.Use (a + b)² = a² + 2ab + b² to find 93².
15. 15.Use (a + b)² = a² + 2ab + b² to find 52².
16. 16.Use (a + b)² = a² + 2ab + b² to find 16².
17. 17.Use (a + b)² = a² + 2ab + b² to find 26².
18. 18.Use (a − b)² = a² − 2ab + b² to find 11².
19. 19.If a − b = 1 and ab = 6, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 68 × 52.
21. 21.Use (a + b)(a − b) = a² − b² to find 41 × 39.
22. 22.Use (a + b)² = a² + 2ab + b² to find 101².
23. 23.Use (a − b)² = a² − 2ab + b² to find 42².
24. 24.Use (a + b)² = a² + 2ab + b² to find 45².
25. 25.Use a² − b² = (a + b)(a − b) to find 33² − 17².
26. 26.Use (a + b)² = a² + 2ab + b² to find 19².
27. 27.Use a² − b² = (a + b)(a − b) to find 24² − 5².
28. 28.Find the value of x² + 2xy + y² when x = 10 and y = 5.
29. 29.Find the value of x² + 2xy + y² when x = 13 and y = 9.
30. 30.If a + b = 9 and ab = 20, what is a² + b²?
31. 31.If a − b = 1 and ab = 2, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 74².
33. 33.If a + b = 7 and ab = 6, what is a² + b²?
34. 34.Find the value of x² + 2xy + y² when x = 8 and y = 3.
35. 35.Use (a + b)(a − b) = a² − b² to find 33 × 27.
36. 36.If a − b = 4 and ab = 77, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 63².
38. 38.If a − b = 5 and ab = 66, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 83².
40. 40.If a − b = 8 and ab = 48, what is a² + b²?

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