Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 253 · 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 99².
2. 2.Find the value of x² − 2xy + y² when x = 13 and y = 2.
3. 3.If a + b = 4 and ab = 3, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 37².
5. 5.Use (a − b)² = a² − 2ab + b² to find 58².
6. 6.If a + b = 11 and ab = 28, what is a² + b²?
7. 7.Use (a + b)² = a² + 2ab + b² to find 17².
8. 8.If a − b = 7 and ab = 18, what is a² + b²?
9. 9.Find the value of x² + 2xy + y² when x = 4 and y = 1.
10. 10.Use (a + b)² = a² + 2ab + b² to find 47².
11. 11.Use (a − b)² = a² − 2ab + b² to find 11².
12. 12.Use (a + b)(a − b) = a² − b² to find 42 × 38.
13. 13.If a − b = 4 and ab = 5, what is a² + b²?
14. 14.Find the value of x² − y² when x = 14 and y = 4.
15. 15.If a − b = 2 and ab = 15, what is a² + b²?
16. 16.Use a² − b² = (a + b)(a − b) to find 64² − 49².
17. 17.Use (a + b)(a − b) = a² − b² to find 22 × 18.
18. 18.Use a² − b² = (a + b)(a − b) to find 80² − 46².
19. 19.Use (a + b)(a − b) = a² − b² to find 86 × 74.
20. 20.Use (a + b)² = a² + 2ab + b² to find 41².
21. 21.Use (a + b)² = a² + 2ab + b² to find 62².
22. 22.If a − b = 9 and ab = 22, what is a² + b²?
23. 23.Find the value of x² − y² when x = 7 and y = 5.
24. 24.Find the value of x² + 2xy + y² when x = 15 and y = 9.
25. 25.Use a² − b² = (a + b)(a − b) to find 34² − 32².
26. 26.If a + b = 8 and ab = 12, what is a² + b²?
27. 27.Use a² − b² = (a + b)(a − b) to find 52² − 37².
28. 28.Use (a − b)² = a² − 2ab + b² to find 39².
29. 29.Use (a + b)² = a² + 2ab + b² to find 83².
30. 30.Use (a + b)² = a² + 2ab + b² to find 64².
31. 31.Use (a + b)(a − b) = a² − b² to find 51 × 49.
32. 32.Use (a + b)(a − b) = a² − b² to find 31 × 29.
33. 33.Use a² − b² = (a + b)(a − b) to find 55² − 19².
34. 34.Use a² − b² = (a + b)(a − b) to find 21² − 13².
35. 35.Use (a − b)² = a² − 2ab + b² to find 21².
36. 36.Use (a + b)² = a² + 2ab + b² to find 67².
37. 37.Find the value of x² + 2xy + y² when x = 4 and y = 2.
38. 38.If a − b = 1 and ab = 132, what is a² + b²?
39. 39.Use a² − b² = (a + b)(a − b) to find 87² − 28².
40. 40.Use (a + b)(a − b) = a² − b² to find 59 × 41.

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