Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 141 · 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 88².
2. 2.Find the value of x² − 2xy + y² when x = 4 and y = 1.
3. 3.Use (a − b)² = a² − 2ab + b² to find 39².
4. 4.Find the value of x² + 2xy + y² when x = 11 and y = 8.
5. 5.If a − b = 1 and ab = 6, what is a² + b²?
6. 6.Use (a − b)² = a² − 2ab + b² to find 48².
7. 7.Use (a − b)² = a² − 2ab + b² to find 75².
8. 8.Use (a + b)² = a² + 2ab + b² to find 72².
9. 9.Use (a + b)² = a² + 2ab + b² to find 41².
10. 10.Use (a + b)² = a² + 2ab + b² to find 104².
11. 11.Use (a + b)(a − b) = a² − b² to find 83 × 77.
12. 12.Use a² − b² = (a + b)(a − b) to find 42² − 4².
13. 13.Use (a − b)² = a² − 2ab + b² to find 41².
14. 14.Use (a + b)² = a² + 2ab + b² to find 93².
15. 15.Use (a − b)² = a² − 2ab + b² to find 95².
16. 16.Use (a − b)² = a² − 2ab + b² to find 66².
17. 17.Use (a + b)² = a² + 2ab + b² to find 52².
18. 18.Use (a − b)² = a² − 2ab + b² to find 57².
19. 19.Use (a + b)² = a² + 2ab + b² to find 48².
20. 20.Use (a + b)(a − b) = a² − b² to find 41 × 39.
21. 21.Use a² − b² = (a + b)(a − b) to find 72² − 34².
22. 22.If a − b = 6 and ab = 16, what is a² + b²?
23. 23.Use (a + b)(a − b) = a² − b² to find 63 × 57.
24. 24.Use (a + b)(a − b) = a² − b² to find 65 × 55.
25. 25.Use a² − b² = (a + b)(a − b) to find 43² − 31².
26. 26.If a − b = 6 and ab = 27, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 78².
28. 28.Use (a + b)² = a² + 2ab + b² to find 34².
29. 29.Find the value of x² + 2xy + y² when x = 5 and y = 3.
30. 30.Use (a + b)(a − b) = a² − b² to find 84 × 76.
31. 31.Use (a + b)² = a² + 2ab + b² to find 92².
32. 32.Use (a − b)² = a² − 2ab + b² to find 22².
33. 33.Use a² − b² = (a + b)(a − b) to find 83² − 2².
34. 34.Use a² − b² = (a + b)(a − b) to find 46² − 8².
35. 35.Use (a − b)² = a² − 2ab + b² to find 37².
36. 36.If a − b = 1 and ab = 2, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 16².
38. 38.Use (a + b)(a − b) = a² − b² to find 55 × 45.
39. 39.Use (a − b)² = a² − 2ab + b² to find 26².
40. 40.Use (a + b)² = a² + 2ab + b² to find 28².

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