Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 742 · 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 = 11 and y = 10.
2. 2.Use (a − b)² = a² − 2ab + b² to find 46².
3. 3.Use (a − b)² = a² − 2ab + b² to find 35².
4. 4.Use (a + b)² = a² + 2ab + b² to find 11².
5. 5.Use (a − b)² = a² − 2ab + b² to find 16².
6. 6.Use (a + b)(a − b) = a² − b² to find 25 × 15.
7. 7.Use (a + b)² = a² + 2ab + b² to find 72².
8. 8.Use (a − b)² = a² − 2ab + b² to find 38².
9. 9.Use (a + b)² = a² + 2ab + b² to find 61².
10. 10.Use (a + b)² = a² + 2ab + b² to find 91².
11. 11.Use (a + b)² = a² + 2ab + b² to find 39².
12. 12.Use (a + b)² = a² + 2ab + b² to find 68².
13. 13.Use (a − b)² = a² − 2ab + b² to find 18².
14. 14.If a + b = 4 and ab = 3, what is a² + b²?
15. 15.Use a² − b² = (a + b)(a − b) to find 88² − 5².
16. 16.Use a² − b² = (a + b)(a − b) to find 54² − 11².
17. 17.Find the value of x² + 2xy + y² when x = 9 and y = 8.
18. 18.Find the value of x² + 2xy + y² when x = 4 and y = 3.
19. 19.Use (a − b)² = a² − 2ab + b² to find 26².
20. 20.If a + b = 7 and ab = 10, what is a² + b²?
21. 21.Use (a + b)(a − b) = a² − b² to find 23 × 17.
22. 22.Use (a − b)² = a² − 2ab + b² to find 89².
23. 23.If a + b = 6 and ab = 8, what is a² + b²?
24. 24.Use (a − b)² = a² − 2ab + b² to find 67².
25. 25.Use (a + b)² = a² + 2ab + b² to find 59².
26. 26.If a + b = 13 and ab = 30, what is a² + b²?
27. 27.If a − b = 5 and ab = 24, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 39 × 21.
29. 29.Find the value of x² − 2xy + y² when x = 11 and y = 2.
30. 30.Use (a − b)² = a² − 2ab + b² to find 31².
31. 31.Use a² − b² = (a + b)(a − b) to find 64² − 18².
32. 32.Find the value of x² + 2xy + y² when x = 3 and y = 1.
33. 33.Use (a + b)(a − b) = a² − b² to find 87 × 73.
34. 34.Use a² − b² = (a + b)(a − b) to find 70² − 11².
35. 35.Use a² − b² = (a + b)(a − b) to find 78² − 67².
36. 36.If a − b = 2 and ab = 80, what is a² + b²?
37. 37.Use (a − b)² = a² − 2ab + b² to find 86².
38. 38.Use a² − b² = (a + b)(a − b) to find 99² − 97².
39. 39.Use (a − b)² = a² − 2ab + b² to find 23².
40. 40.Use (a + b)² = a² + 2ab + b² to find 67².

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