Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 853 · 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 = 6 and y = 5.
2. 2.If a + b = 16 and ab = 60, what is a² + b²?
3. 3.If a + b = 3 and ab = 2, what is a² + b²?
4. 4.Use (a + b)² = a² + 2ab + b² to find 51².
5. 5.Use (a + b)² = a² + 2ab + b² to find 94².
6. 6.If a + b = 12 and ab = 11, what is a² + b²?
7. 7.Find the value of x² − 2xy + y² when x = 15 and y = 4.
8. 8.Use (a − b)² = a² − 2ab + b² to find 39².
9. 9.Use (a + b)² = a² + 2ab + b² to find 89².
10. 10.If a − b = 1 and ab = 90, what is a² + b²?
11. 11.Use (a − b)² = a² − 2ab + b² to find 27².
12. 12.Use (a + b)² = a² + 2ab + b² to find 93².
13. 13.Use a² − b² = (a + b)(a − b) to find 40² − 17².
14. 14.Use a² − b² = (a + b)(a − b) to find 66² − 65².
15. 15.Use (a + b)(a − b) = a² − b² to find 62 × 58.
16. 16.Find the value of x² − y² when x = 15 and y = 6.
17. 17.Use (a + b)(a − b) = a² − b² to find 55 × 45.
18. 18.Use (a + b)² = a² + 2ab + b² to find 43².
19. 19.Use a² − b² = (a + b)(a − b) to find 30² − 13².
20. 20.Find the value of x² − y² when x = 7 and y = 2.
21. 21.Use (a + b)² = a² + 2ab + b² to find 82².
22. 22.Use (a − b)² = a² − 2ab + b² to find 17².
23. 23.Find the value of x² + 2xy + y² when x = 4 and y = 1.
24. 24.Use a² − b² = (a + b)(a − b) to find 92² − 48².
25. 25.Use a² − b² = (a + b)(a − b) to find 22² − 6².
26. 26.If a + b = 9 and ab = 20, what is a² + b²?
27. 27.Use (a − b)² = a² − 2ab + b² to find 89².
28. 28.Use a² − b² = (a + b)(a − b) to find 40² − 13².
29. 29.Use (a + b)² = a² + 2ab + b² to find 95².
30. 30.Use (a + b)(a − b) = a² − b² to find 74 × 66.
31. 31.Use (a + b)² = a² + 2ab + b² to find 107².
32. 32.Use (a + b)(a − b) = a² − b² to find 54 × 46.
33. 33.Find the value of x² + 2xy + y² when x = 11 and y = 9.
34. 34.Use a² − b² = (a + b)(a − b) to find 54² − 53².
35. 35.If a + b = 8 and ab = 12, what is a² + b²?
36. 36.Use a² − b² = (a + b)(a − b) to find 64² − 5².
37. 37.Use (a − b)² = a² − 2ab + b² to find 75².
38. 38.Use (a − b)² = a² − 2ab + b² to find 92².
39. 39.Find the value of x² + 2xy + y² when x = 3 and y = 2.
40. 40.Use a² − b² = (a + b)(a − b) to find 81² − 45².

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