Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 416 · 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 86².
2. 2.Use (a − b)² = a² − 2ab + b² to find 37².
3. 3.Use a² − b² = (a + b)(a − b) to find 39² − 34².
4. 4.Use (a + b)² = a² + 2ab + b² to find 23².
5. 5.Use (a − b)² = a² − 2ab + b² to find 61².
6. 6.Use (a + b)(a − b) = a² − b² to find 103 × 97.
7. 7.Use (a + b)(a − b) = a² − b² to find 26 × 14.
8. 8.Use a² − b² = (a + b)(a − b) to find 32² − 3².
9. 9.Use (a + b)² = a² + 2ab + b² to find 55².
10. 10.Use a² − b² = (a + b)(a − b) to find 67² − 39².
11. 11.Find the value of x² − y² when x = 7 and y = 4.
12. 12.Use a² − b² = (a + b)(a − b) to find 88² − 49².
13. 13.Use a² − b² = (a + b)(a − b) to find 23² − 21².
14. 14.Find the value of x² + 2xy + y² when x = 3 and y = 2.
15. 15.Use (a + b)(a − b) = a² − b² to find 28 × 12.
16. 16.Use (a + b)(a − b) = a² − b² to find 41 × 39.
17. 17.Use a² − b² = (a + b)(a − b) to find 24² − 6².
18. 18.Use (a + b)(a − b) = a² − b² to find 23 × 17.
19. 19.Use a² − b² = (a + b)(a − b) to find 21² − 16².
20. 20.Use (a + b)(a − b) = a² − b² to find 39 × 21.
21. 21.Use (a − b)² = a² − 2ab + b² to find 66².
22. 22.Use (a + b)(a − b) = a² − b² to find 65 × 55.
23. 23.Use a² − b² = (a + b)(a − b) to find 95² − 94².
24. 24.Find the value of x² + 2xy + y² when x = 4 and y = 3.
25. 25.Use (a + b)² = a² + 2ab + b² to find 24².
26. 26.Find the value of x² − 2xy + y² when x = 12 and y = 2.
27. 27.Use (a + b)² = a² + 2ab + b² to find 22².
28. 28.If a − b = 3 and ab = 10, what is a² + b²?
29. 29.Find the value of x² − 2xy + y² when x = 12 and y = 1.
30. 30.Use (a + b)(a − b) = a² − b² to find 89 × 71.
31. 31.If a − b = 8 and ab = 33, what is a² + b²?
32. 32.Use (a + b)(a − b) = a² − b² to find 105 × 95.
33. 33.Use a² − b² = (a + b)(a − b) to find 93² − 60².
34. 34.Use a² − b² = (a + b)(a − b) to find 98² − 79².
35. 35.Use (a − b)² = a² − 2ab + b² to find 46².
36. 36.Use a² − b² = (a + b)(a − b) to find 31² − 2².
37. 37.If a + b = 3 and ab = 2, what is a² + b²?
38. 38.Use a² − b² = (a + b)(a − b) to find 61² − 4².
39. 39.Use (a + b)² = a² + 2ab + b² to find 17².
40. 40.If a + b = 6 and ab = 5, what is a² + b²?

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