Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 406 · 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 106².
2. 2.Use (a − b)² = a² − 2ab + b² to find 28².
3. 3.Use a² − b² = (a + b)(a − b) to find 86² − 63².
4. 4.Find the value of x² − y² when x = 5 and y = 2.
5. 5.If a − b = 4 and ab = 21, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 27².
7. 7.Use (a − b)² = a² − 2ab + b² to find 21².
8. 8.Use (a + b)(a − b) = a² − b² to find 65 × 55.
9. 9.If a − b = 2 and ab = 3, what is a² + b²?
10. 10.If a − b = 6 and ab = 27, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 59².
12. 12.Use (a − b)² = a² − 2ab + b² to find 26².
13. 13.Use (a − b)² = a² − 2ab + b² to find 69².
14. 14.Use (a + b)(a − b) = a² − b² to find 28 × 12.
15. 15.Find the value of x² + 2xy + y² when x = 5 and y = 4.
16. 16.Find the value of x² − 2xy + y² when x = 5 and y = 4.
17. 17.Use a² − b² = (a + b)(a − b) to find 46² − 43².
18. 18.Use a² − b² = (a + b)(a − b) to find 83² − 32².
19. 19.Use (a + b)² = a² + 2ab + b² to find 25².
20. 20.If a + b = 14 and ab = 40, what is a² + b²?
21. 21.Find the value of x² + 2xy + y² when x = 8 and y = 4.
22. 22.Find the value of x² − 2xy + y² when x = 8 and y = 4.
23. 23.Use a² − b² = (a + b)(a − b) to find 26² − 23².
24. 24.Use (a + b)² = a² + 2ab + b² to find 57².
25. 25.Use (a + b)(a − b) = a² − b² to find 72 × 68.
26. 26.Use (a + b)(a − b) = a² − b² to find 25 × 15.
27. 27.Find the value of x² + 2xy + y² when x = 15 and y = 6.
28. 28.Use (a + b)² = a² + 2ab + b² to find 102².
29. 29.Use (a + b)(a − b) = a² − b² to find 61 × 59.
30. 30.Use a² − b² = (a + b)(a − b) to find 99² − 96².
31. 31.Use (a + b)(a − b) = a² − b² to find 92 × 88.
32. 32.Use (a + b)² = a² + 2ab + b² to find 104².
33. 33.Use (a − b)² = a² − 2ab + b² to find 25².
34. 34.Use (a − b)² = a² − 2ab + b² to find 67².
35. 35.Find the value of x² − y² when x = 4 and y = 1.
36. 36.Use (a − b)² = a² − 2ab + b² to find 37².
37. 37.Use (a − b)² = a² − 2ab + b² to find 89².
38. 38.Find the value of x² − 2xy + y² when x = 15 and y = 2.
39. 39.Find the value of x² − 2xy + y² when x = 6 and y = 2.
40. 40.Use a² − b² = (a + b)(a − b) to find 61² − 9².

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