Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 566 · 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.Use a² − b² = (a + b)(a − b) to find 91² − 39².
2. 2.Use a² − b² = (a + b)(a − b) to find 30² − 13².
3. 3.Find the value of x² + 2xy + y² when x = 8 and y = 6.
4. 4.Find the value of x² + 2xy + y² when x = 13 and y = 4.
5. 5.If a + b = 8 and ab = 12, what is a² + b²?
6. 6.Use (a + b)(a − b) = a² − b² to find 106 × 94.
7. 7.Use (a + b)² = a² + 2ab + b² to find 92².
8. 8.Find the value of x² + 2xy + y² when x = 15 and y = 1.
9. 9.Use a² − b² = (a + b)(a − b) to find 41² − 36².
10. 10.Find the value of x² − y² when x = 9 and y = 3.
11. 11.Use (a − b)² = a² − 2ab + b² to find 75².
12. 12.Use a² − b² = (a + b)(a − b) to find 59² − 25².
13. 13.If a − b = 1 and ab = 110, what is a² + b²?
14. 14.Use (a − b)² = a² − 2ab + b² to find 26².
15. 15.Find the value of x² − y² when x = 13 and y = 4.
16. 16.Find the value of x² − 2xy + y² when x = 10 and y = 1.
17. 17.Use a² − b² = (a + b)(a − b) to find 28² − 23².
18. 18.Find the value of x² + 2xy + y² when x = 7 and y = 6.
19. 19.Find the value of x² − y² when x = 13 and y = 12.
20. 20.Use (a + b)(a − b) = a² − b² to find 53 × 47.
21. 21.If a + b = 16 and ab = 63, what is a² + b²?
22. 22.Use (a − b)² = a² − 2ab + b² to find 71².
23. 23.Use (a + b)² = a² + 2ab + b² to find 78².
24. 24.Find the value of x² − 2xy + y² when x = 15 and y = 6.
25. 25.Use (a + b)² = a² + 2ab + b² to find 34².
26. 26.Use (a − b)² = a² − 2ab + b² to find 91².
27. 27.Use (a + b)² = a² + 2ab + b² to find 47².
28. 28.Use (a + b)² = a² + 2ab + b² to find 23².
29. 29.Use (a + b)(a − b) = a² − b² to find 68 × 52.
30. 30.Use a² − b² = (a + b)(a − b) to find 81² − 71².
31. 31.Find the value of x² + 2xy + y² when x = 13 and y = 12.
32. 32.Use (a + b)(a − b) = a² − b² to find 78 × 62.
33. 33.Use (a + b)² = a² + 2ab + b² to find 86².
34. 34.Use (a + b)² = a² + 2ab + b² to find 93².
35. 35.Use (a − b)² = a² − 2ab + b² to find 18².
36. 36.Use a² − b² = (a + b)(a − b) to find 35² − 7².
37. 37.Use (a + b)(a − b) = a² − b² to find 35 × 25.
38. 38.Use (a − b)² = a² − 2ab + b² to find 22².
39. 39.Use (a + b)(a − b) = a² − b² to find 42 × 38.
40. 40.If a − b = 1 and ab = 2, what is a² + b²?

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