Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 792 · 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.If a + b = 13 and ab = 36, what is a² + b²?
2. 2.Use (a + b)² = a² + 2ab + b² to find 71².
3. 3.Use (a + b)(a − b) = a² − b² to find 34 × 26.
4. 4.If a + b = 6 and ab = 8, what is a² + b²?
5. 5.Use (a + b)² = a² + 2ab + b² to find 107².
6. 6.Use (a − b)² = a² − 2ab + b² to find 33².
7. 7.Use (a − b)² = a² − 2ab + b² to find 24².
8. 8.Use (a + b)(a − b) = a² − b² to find 53 × 47.
9. 9.Use (a − b)² = a² − 2ab + b² to find 68².
10. 10.Use (a + b)² = a² + 2ab + b² to find 32².
11. 11.Find the value of x² − 2xy + y² when x = 5 and y = 1.
12. 12.Find the value of x² − y² when x = 4 and y = 2.
13. 13.Use (a + b)(a − b) = a² − b² to find 56 × 44.
14. 14.Find the value of x² − y² when x = 12 and y = 11.
15. 15.Use a² − b² = (a + b)(a − b) to find 62² − 41².
16. 16.If a + b = 22 and ab = 120, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 94².
18. 18.Use (a + b)² = a² + 2ab + b² to find 103².
19. 19.Use (a − b)² = a² − 2ab + b² to find 81².
20. 20.Find the value of x² − y² when x = 11 and y = 8.
21. 21.If a + b = 8 and ab = 15, what is a² + b²?
22. 22.Find the value of x² − y² when x = 14 and y = 6.
23. 23.Use (a + b)² = a² + 2ab + b² to find 33².
24. 24.Use (a + b)² = a² + 2ab + b² to find 69².
25. 25.Use (a + b)² = a² + 2ab + b² to find 11².
26. 26.Use a² − b² = (a + b)(a − b) to find 31² − 1².
27. 27.Use a² − b² = (a + b)(a − b) to find 31² − 6².
28. 28.Find the value of x² + 2xy + y² when x = 7 and y = 5.
29. 29.Use a² − b² = (a + b)(a − b) to find 78² − 39².
30. 30.If a + b = 15 and ab = 54, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 61 × 59.
32. 32.Use (a + b)(a − b) = a² − b² to find 32 × 28.
33. 33.Use (a + b)² = a² + 2ab + b² to find 42².
34. 34.Use (a + b)(a − b) = a² − b² to find 31 × 29.
35. 35.Use a² − b² = (a + b)(a − b) to find 33² − 30².
36. 36.Use (a − b)² = a² − 2ab + b² to find 15².
37. 37.Use (a + b)(a − b) = a² − b² to find 55 × 45.
38. 38.Use (a − b)² = a² − 2ab + b² to find 52².
39. 39.Use (a − b)² = a² − 2ab + b² to find 13².
40. 40.If a + b = 4 and ab = 3, what is a² + b²?

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