Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 139 · 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 28².
2. 2.Use a² − b² = (a + b)(a − b) to find 54² − 42².
3. 3.Use (a − b)² = a² − 2ab + b² to find 59².
4. 4.Use (a − b)² = a² − 2ab + b² to find 63².
5. 5.If a − b = 2 and ab = 3, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 82².
7. 7.Find the value of x² − 2xy + y² when x = 7 and y = 3.
8. 8.Use (a − b)² = a² − 2ab + b² to find 56².
9. 9.Find the value of x² − y² when x = 9 and y = 3.
10. 10.Use (a − b)² = a² − 2ab + b² to find 58².
11. 11.Use (a + b)² = a² + 2ab + b² to find 14².
12. 12.Find the value of x² − 2xy + y² when x = 4 and y = 1.
13. 13.Use a² − b² = (a + b)(a − b) to find 41² − 33².
14. 14.Use a² − b² = (a + b)(a − b) to find 37² − 12².
15. 15.Use a² − b² = (a + b)(a − b) to find 31² − 25².
16. 16.Find the value of x² − 2xy + y² when x = 11 and y = 6.
17. 17.Use (a + b)(a − b) = a² − b² to find 103 × 97.
18. 18.Use (a + b)(a − b) = a² − b² to find 95 × 85.
19. 19.Use (a − b)² = a² − 2ab + b² to find 37².
20. 20.Use (a + b)(a − b) = a² − b² to find 23 × 17.
21. 21.If a − b = 5 and ab = 24, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 69².
23. 23.Use (a + b)(a − b) = a² − b² to find 31 × 29.
24. 24.Use (a + b)² = a² + 2ab + b² to find 52².
25. 25.Use (a + b)² = a² + 2ab + b² to find 58².
26. 26.Use (a − b)² = a² − 2ab + b² to find 67².
27. 27.Find the value of x² − 2xy + y² when x = 4 and y = 2.
28. 28.If a + b = 5 and ab = 6, what is a² + b²?
29. 29.If a + b = 14 and ab = 45, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 98².
31. 31.Use (a + b)(a − b) = a² − b² to find 36 × 24.
32. 32.Use (a − b)² = a² − 2ab + b² to find 43².
33. 33.If a + b = 3 and ab = 2, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 107 × 93.
35. 35.Use (a + b)(a − b) = a² − b² to find 52 × 48.
36. 36.Use (a − b)² = a² − 2ab + b² to find 93².
37. 37.Find the value of x² + 2xy + y² when x = 9 and y = 6.
38. 38.Find the value of x² − 2xy + y² when x = 14 and y = 13.
39. 39.Use (a − b)² = a² − 2ab + b² to find 94².
40. 40.If a − b = 3 and ab = 4, what is a² + b²?

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