Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 67 · 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 = 5 and y = 1.
2. 2.Use a² − b² = (a + b)(a − b) to find 34² − 16².
3. 3.Use (a − b)² = a² − 2ab + b² to find 36².
4. 4.Use (a + b)² = a² + 2ab + b² to find 17².
5. 5.Use (a − b)² = a² − 2ab + b² to find 64².
6. 6.Use (a + b)(a − b) = a² − b² to find 57 × 43.
7. 7.Use (a + b)(a − b) = a² − b² to find 88 × 72.
8. 8.Use (a + b)(a − b) = a² − b² to find 105 × 95.
9. 9.Use (a + b)² = a² + 2ab + b² to find 72².
10. 10.Use (a − b)² = a² − 2ab + b² to find 19².
11. 11.Use (a + b)² = a² + 2ab + b² to find 88².
12. 12.Use a² − b² = (a + b)(a − b) to find 37² − 6².
13. 13.Use (a + b)² = a² + 2ab + b² to find 105².
14. 14.Use (a + b)(a − b) = a² − b² to find 83 × 77.
15. 15.Use (a + b)(a − b) = a² − b² to find 36 × 24.
16. 16.If a − b = 2 and ab = 48, what is a² + b²?
17. 17.Use a² − b² = (a + b)(a − b) to find 35² − 20².
18. 18.Use (a − b)² = a² − 2ab + b² to find 16².
19. 19.Use (a + b)² = a² + 2ab + b² to find 64².
20. 20.Use a² − b² = (a + b)(a − b) to find 24² − 4².
21. 21.Use a² − b² = (a + b)(a − b) to find 69² − 54².
22. 22.Use (a − b)² = a² − 2ab + b² to find 14².
23. 23.Use (a + b)² = a² + 2ab + b² to find 83².
24. 24.Use (a − b)² = a² − 2ab + b² to find 77².
25. 25.If a − b = 1 and ab = 2, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 33².
27. 27.Use (a + b)(a − b) = a² − b² to find 47 × 33.
28. 28.Use (a − b)² = a² − 2ab + b² to find 78².
29. 29.Use (a + b)² = a² + 2ab + b² to find 95².
30. 30.Use (a − b)² = a² − 2ab + b² to find 43².
31. 31.Use (a − b)² = a² − 2ab + b² to find 49².
32. 32.Use (a − b)² = a² − 2ab + b² to find 39².
33. 33.Use (a + b)² = a² + 2ab + b² to find 85².
34. 34.Use a² − b² = (a + b)(a − b) to find 32² − 11².
35. 35.If a − b = 5 and ab = 6, what is a² + b²?
36. 36.Use (a − b)² = a² − 2ab + b² to find 99².
37. 37.Use a² − b² = (a + b)(a − b) to find 63² − 54².
38. 38.If a + b = 3 and ab = 2, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 61² − 28².
40. 40.Use (a + b)(a − b) = a² − b² to find 44 × 36.

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