Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 799 · 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 = 1 and ab = 132, what is a² + b²?
2. 2.Use (a + b)(a − b) = a² − b² to find 33 × 27.
3. 3.Use (a − b)² = a² − 2ab + b² to find 26².
4. 4.Use a² − b² = (a + b)(a − b) to find 48² − 17².
5. 5.Find the value of x² + 2xy + y² when x = 13 and y = 5.
6. 6.Use (a + b)(a − b) = a² − b² to find 32 × 28.
7. 7.Use (a + b)² = a² + 2ab + b² to find 51².
8. 8.Use (a + b)(a − b) = a² − b² to find 103 × 97.
9. 9.If a − b = 2 and ab = 8, what is a² + b²?
10. 10.Use (a − b)² = a² − 2ab + b² to find 14².
11. 11.Use (a − b)² = a² − 2ab + b² to find 12².
12. 12.Use (a + b)² = a² + 2ab + b² to find 92².
13. 13.Use a² − b² = (a + b)(a − b) to find 34² − 1².
14. 14.Find the value of x² − y² when x = 5 and y = 2.
15. 15.If a + b = 21 and ab = 110, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 26².
17. 17.Use (a + b)(a − b) = a² − b² to find 55 × 45.
18. 18.Use (a − b)² = a² − 2ab + b² to find 37².
19. 19.If a − b = 2 and ab = 3, what is a² + b²?
20. 20.If a + b = 17 and ab = 60, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 63² − 2².
22. 22.Find the value of x² + 2xy + y² when x = 15 and y = 3.
23. 23.Find the value of x² − y² when x = 6 and y = 3.
24. 24.Use (a + b)(a − b) = a² − b² to find 36 × 24.
25. 25.Use (a + b)² = a² + 2ab + b² to find 24².
26. 26.Use (a + b)² = a² + 2ab + b² to find 101².
27. 27.Use (a + b)(a − b) = a² − b² to find 86 × 74.
28. 28.Use (a − b)² = a² − 2ab + b² to find 91².
29. 29.Use a² − b² = (a + b)(a − b) to find 38² − 27².
30. 30.Find the value of x² − y² when x = 5 and y = 4.
31. 31.Use (a + b)(a − b) = a² − b² to find 89 × 71.
32. 32.Use a² − b² = (a + b)(a − b) to find 31² − 3².
33. 33.Find the value of x² + 2xy + y² when x = 9 and y = 5.
34. 34.Find the value of x² − 2xy + y² when x = 10 and y = 4.
35. 35.Use a² − b² = (a + b)(a − b) to find 81² − 39².
36. 36.Use a² − b² = (a + b)(a − b) to find 25² − 15².
37. 37.Use (a − b)² = a² − 2ab + b² to find 84².
38. 38.If a + b = 13 and ab = 40, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 89².
40. 40.Use (a + b)(a − b) = a² − b² to find 57 × 43.

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