Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 949 · 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 = 4 and ab = 12, what is a² + b²?
2. 2.Use a² − b² = (a + b)(a − b) to find 90² − 45².
3. 3.If a + b = 5 and ab = 4, what is a² + b²?
4. 4.If a + b = 10 and ab = 16, what is a² + b²?
5. 5.If a + b = 7 and ab = 12, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 56².
7. 7.Use (a + b)(a − b) = a² − b² to find 35 × 25.
8. 8.Find the value of x² − 2xy + y² when x = 3 and y = 1.
9. 9.Find the value of x² + 2xy + y² when x = 13 and y = 6.
10. 10.Use a² − b² = (a + b)(a − b) to find 73² − 17².
11. 11.Find the value of x² − y² when x = 3 and y = 1.
12. 12.Use (a − b)² = a² − 2ab + b² to find 51².
13. 13.Use (a + b)(a − b) = a² − b² to find 83 × 77.
14. 14.Use (a + b)(a − b) = a² − b² to find 56 × 44.
15. 15.Find the value of x² + 2xy + y² when x = 13 and y = 9.
16. 16.Use a² − b² = (a + b)(a − b) to find 32² − 27².
17. 17.Find the value of x² − y² when x = 13 and y = 5.
18. 18.Use (a + b)² = a² + 2ab + b² to find 47².
19. 19.Use (a + b)(a − b) = a² − b² to find 109 × 91.
20. 20.If a − b = 4 and ab = 60, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 32 × 28.
22. 22.Find the value of x² + 2xy + y² when x = 13 and y = 11.
23. 23.Use (a + b)² = a² + 2ab + b² to find 38².
24. 24.Use (a − b)² = a² − 2ab + b² to find 43².
25. 25.Use (a + b)(a − b) = a² − b² to find 76 × 64.
26. 26.If a + b = 4 and ab = 3, what is a² + b²?
27. 27.Find the value of x² − y² when x = 8 and y = 3.
28. 28.Use (a + b)(a − b) = a² − b² to find 82 × 78.
29. 29.Use a² − b² = (a + b)(a − b) to find 61² − 36².
30. 30.Use (a − b)² = a² − 2ab + b² to find 14².
31. 31.If a + b = 3 and ab = 2, what is a² + b²?
32. 32.Use (a + b)² = a² + 2ab + b² to find 71².
33. 33.Use a² − b² = (a + b)(a − b) to find 48² − 35².
34. 34.Use (a − b)² = a² − 2ab + b² to find 84².
35. 35.Use (a − b)² = a² − 2ab + b² to find 18².
36. 36.Use a² − b² = (a + b)(a − b) to find 49² − 40².
37. 37.Find the value of x² − 2xy + y² when x = 15 and y = 3.
38. 38.Use a² − b² = (a + b)(a − b) to find 21² − 6².
39. 39.Find the value of x² + 2xy + y² when x = 13 and y = 4.
40. 40.Use a² − b² = (a + b)(a − b) to find 60² − 6².

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