Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 52 · 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 41².
2. 2.Use (a + b)² = a² + 2ab + b² to find 55².
3. 3.Find the value of x² − y² when x = 14 and y = 8.
4. 4.Use (a + b)(a − b) = a² − b² to find 33 × 27.
5. 5.Use (a + b)² = a² + 2ab + b² to find 96².
6. 6.Use (a + b)(a − b) = a² − b² to find 61 × 59.
7. 7.Use (a + b)(a − b) = a² − b² to find 99 × 81.
8. 8.Use (a + b)² = a² + 2ab + b² to find 71².
9. 9.Find the value of x² + 2xy + y² when x = 6 and y = 3.
10. 10.Use a² − b² = (a + b)(a − b) to find 87² − 61².
11. 11.Use (a + b)(a − b) = a² − b² to find 101 × 99.
12. 12.Use (a + b)² = a² + 2ab + b² to find 79².
13. 13.Use (a + b)(a − b) = a² − b² to find 48 × 32.
14. 14.Use (a + b)² = a² + 2ab + b² to find 61².
15. 15.Use (a − b)² = a² − 2ab + b² to find 66².
16. 16.Use (a + b)(a − b) = a² − b² to find 94 × 86.
17. 17.Find the value of x² − 2xy + y² when x = 15 and y = 12.
18. 18.Use (a + b)(a − b) = a² − b² to find 24 × 16.
19. 19.Use a² − b² = (a + b)(a − b) to find 98² − 54².
20. 20.Use (a + b)(a − b) = a² − b² to find 85 × 75.
21. 21.Use (a − b)² = a² − 2ab + b² to find 37².
22. 22.If a − b = 1 and ab = 90, what is a² + b²?
23. 23.Find the value of x² − 2xy + y² when x = 10 and y = 7.
24. 24.Use a² − b² = (a + b)(a − b) to find 41² − 6².
25. 25.Use a² − b² = (a + b)(a − b) to find 80² − 56².
26. 26.Use (a + b)(a − b) = a² − b² to find 65 × 55.
27. 27.Find the value of x² − y² when x = 5 and y = 2.
28. 28.Find the value of x² + 2xy + y² when x = 13 and y = 11.
29. 29.If a + b = 12 and ab = 32, what is a² + b²?
30. 30.Use (a + b)² = a² + 2ab + b² to find 45².
31. 31.Use (a + b)(a − b) = a² − b² to find 78 × 62.
32. 32.Use (a + b)(a − b) = a² − b² to find 38 × 22.
33. 33.Use (a + b)² = a² + 2ab + b² to find 98².
34. 34.If a − b = 3 and ab = 4, what is a² + b²?
35. 35.Use a² − b² = (a + b)(a − b) to find 48² − 43².
36. 36.Use (a + b)² = a² + 2ab + b² to find 78².
37. 37.Use a² − b² = (a + b)(a − b) to find 78² − 13².
38. 38.Use (a − b)² = a² − 2ab + b² to find 27².
39. 39.Use (a + b)(a − b) = a² − b² to find 92 × 88.
40. 40.Use a² − b² = (a + b)(a − b) to find 37² − 32².

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