Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 223 · 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.Find the value of x² + 2xy + y² when x = 8 and y = 3.
2. 2.Use a² − b² = (a + b)(a − b) to find 52² − 10².
3. 3.Use a² − b² = (a + b)(a − b) to find 65² − 23².
4. 4.Use (a + b)² = a² + 2ab + b² to find 41².
5. 5.Use (a + b)(a − b) = a² − b² to find 23 × 17.
6. 6.Use (a − b)² = a² − 2ab + b² to find 18².
7. 7.If a + b = 11 and ab = 28, what is a² + b²?
8. 8.Use (a + b)(a − b) = a² − b² to find 59 × 41.
9. 9.Use a² − b² = (a + b)(a − b) to find 30² − 21².
10. 10.Use a² − b² = (a + b)(a − b) to find 42² − 17².
11. 11.Use (a − b)² = a² − 2ab + b² to find 81².
12. 12.Use a² − b² = (a + b)(a − b) to find 36² − 30².
13. 13.Use (a − b)² = a² − 2ab + b² to find 94².
14. 14.Use a² − b² = (a + b)(a − b) to find 35² − 15².
15. 15.Use (a + b)(a − b) = a² − b² to find 83 × 77.
16. 16.Use (a − b)² = a² − 2ab + b² to find 68².
17. 17.Use (a + b)(a − b) = a² − b² to find 101 × 99.
18. 18.Find the value of x² + 2xy + y² when x = 10 and y = 1.
19. 19.Find the value of x² − 2xy + y² when x = 9 and y = 3.
20. 20.If a + b = 18 and ab = 72, what is a² + b²?
21. 21.Use (a − b)² = a² − 2ab + b² to find 35².
22. 22.If a − b = 5 and ab = 50, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 99 × 81.
24. 24.Use (a − b)² = a² − 2ab + b² to find 62².
25. 25.Use (a + b)(a − b) = a² − b² to find 64 × 56.
26. 26.Use (a + b)² = a² + 2ab + b² to find 18².
27. 27.If a + b = 12 and ab = 27, what is a² + b²?
28. 28.Find the value of x² − y² when x = 7 and y = 1.
29. 29.Use (a − b)² = a² − 2ab + b² to find 73².
30. 30.Use a² − b² = (a + b)(a − b) to find 38² − 14².
31. 31.Find the value of x² − y² when x = 7 and y = 6.
32. 32.Find the value of x² + 2xy + y² when x = 3 and y = 2.
33. 33.Use a² − b² = (a + b)(a − b) to find 48² − 30².
34. 34.Use (a + b)² = a² + 2ab + b² to find 11².
35. 35.Find the value of x² + 2xy + y² when x = 9 and y = 8.
36. 36.Find the value of x² − y² when x = 11 and y = 1.
37. 37.Use (a + b)² = a² + 2ab + b² to find 43².
38. 38.Use (a + b)² = a² + 2ab + b² to find 31².
39. 39.Use (a + b)² = a² + 2ab + b² to find 34².
40. 40.Use (a + b)² = a² + 2ab + b² to find 38².

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