Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 513 · 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 = 10 and y = 7.
2. 2.Use (a + b)² = a² + 2ab + b² to find 72².
3. 3.Use (a + b)² = a² + 2ab + b² to find 25².
4. 4.Use (a + b)² = a² + 2ab + b² to find 74².
5. 5.Use (a − b)² = a² − 2ab + b² to find 86².
6. 6.Use (a + b)² = a² + 2ab + b² to find 13².
7. 7.Use (a + b)² = a² + 2ab + b² to find 31².
8. 8.Use (a − b)² = a² − 2ab + b² to find 23².
9. 9.Use a² − b² = (a + b)(a − b) to find 48² − 32².
10. 10.Use (a + b)(a − b) = a² − b² to find 62 × 58.
11. 11.Use (a + b)² = a² + 2ab + b² to find 108².
12. 12.Use (a + b)(a − b) = a² − b² to find 69 × 51.
13. 13.Use a² − b² = (a + b)(a − b) to find 39² − 11².
14. 14.Use (a + b)² = a² + 2ab + b² to find 29².
15. 15.Find the value of x² − y² when x = 13 and y = 5.
16. 16.If a + b = 10 and ab = 9, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 28².
18. 18.Use a² − b² = (a + b)(a − b) to find 58² − 44².
19. 19.Use (a + b)(a − b) = a² − b² to find 74 × 66.
20. 20.Use (a + b)(a − b) = a² − b² to find 55 × 45.
21. 21.Use (a − b)² = a² − 2ab + b² to find 29².
22. 22.Use (a + b)(a − b) = a² − b² to find 81 × 79.
23. 23.Use (a − b)² = a² − 2ab + b² to find 66².
24. 24.Use (a + b)(a − b) = a² − b² to find 108 × 92.
25. 25.Use (a + b)² = a² + 2ab + b² to find 56².
26. 26.Find the value of x² − 2xy + y² when x = 9 and y = 1.
27. 27.Use (a + b)² = a² + 2ab + b² to find 62².
28. 28.If a − b = 1 and ab = 2, what is a² + b²?
29. 29.If a + b = 5 and ab = 6, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 45².
31. 31.If a − b = 1 and ab = 30, what is a² + b²?
32. 32.Use a² − b² = (a + b)(a − b) to find 76² − 63².
33. 33.Use (a + b)(a − b) = a² − b² to find 35 × 25.
34. 34.If a − b = 3 and ab = 88, what is a² + b²?
35. 35.Use (a − b)² = a² − 2ab + b² to find 33².
36. 36.Use (a + b)(a − b) = a² − b² to find 102 × 98.
37. 37.Use (a + b)(a − b) = a² − b² to find 43 × 37.
38. 38.Find the value of x² − 2xy + y² when x = 15 and y = 12.
39. 39.Use a² − b² = (a + b)(a − b) to find 49² − 24².
40. 40.If a − b = 1 and ab = 6, what is a² + b²?

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