Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 821 · 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 = 8 and y = 5.
2. 2.If a − b = 1 and ab = 6, what is a² + b²?
3. 3.Use a² − b² = (a + b)(a − b) to find 78² − 60².
4. 4.Use (a − b)² = a² − 2ab + b² to find 33².
5. 5.Use (a + b)² = a² + 2ab + b² to find 39².
6. 6.Use (a + b)(a − b) = a² − b² to find 43 × 37.
7. 7.Use (a − b)² = a² − 2ab + b² to find 83².
8. 8.Use (a − b)² = a² − 2ab + b² to find 71².
9. 9.If a + b = 14 and ab = 40, what is a² + b²?
10. 10.Use (a + b)(a − b) = a² − b² to find 32 × 28.
11. 11.Find the value of x² − 2xy + y² when x = 10 and y = 1.
12. 12.Use a² − b² = (a + b)(a − b) to find 96² − 11².
13. 13.Use (a − b)² = a² − 2ab + b² to find 36².
14. 14.Use (a + b)(a − b) = a² − b² to find 42 × 38.
15. 15.Use (a − b)² = a² − 2ab + b² to find 97².
16. 16.Use (a + b)(a − b) = a² − b² to find 58 × 42.
17. 17.Use (a + b)² = a² + 2ab + b² to find 35².
18. 18.Use a² − b² = (a + b)(a − b) to find 35² − 25².
19. 19.Use (a + b)² = a² + 2ab + b² to find 74².
20. 20.Use (a − b)² = a² − 2ab + b² to find 18².
21. 21.If a + b = 18 and ab = 80, what is a² + b²?
22. 22.Use (a + b)² = a² + 2ab + b² to find 67².
23. 23.Use (a + b)(a − b) = a² − b² to find 41 × 39.
24. 24.Use (a + b)(a − b) = a² − b² to find 61 × 59.
25. 25.If a − b = 6 and ab = 7, what is a² + b²?
26. 26.Use (a − b)² = a² − 2ab + b² to find 35².
27. 27.Use a² − b² = (a + b)(a − b) to find 81² − 25².
28. 28.Find the value of x² − 2xy + y² when x = 15 and y = 9.
29. 29.Use a² − b² = (a + b)(a − b) to find 23² − 5².
30. 30.If a − b = 4 and ab = 5, what is a² + b²?
31. 31.Use (a + b)(a − b) = a² − b² to find 55 × 45.
32. 32.If a − b = 9 and ab = 36, what is a² + b²?
33. 33.Use a² − b² = (a + b)(a − b) to find 68² − 9².
34. 34.Find the value of x² + 2xy + y² when x = 4 and y = 3.
35. 35.Find the value of x² + 2xy + y² when x = 6 and y = 2.
36. 36.If a − b = 1 and ab = 132, what is a² + b²?
37. 37.If a + b = 13 and ab = 36, what is a² + b²?
38. 38.If a − b = 5 and ab = 6, what is a² + b²?
39. 39.Use (a + b)(a − b) = a² − b² to find 33 × 27.
40. 40.Use (a + b)(a − b) = a² − b² to find 96 × 84.

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