Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 781 · 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 = 7 and y = 1.
2. 2.Use (a + b)² = a² + 2ab + b² to find 39².
3. 3.Use a² − b² = (a + b)(a − b) to find 86² − 22².
4. 4.Use (a + b)(a − b) = a² − b² to find 49 × 31.
5. 5.Use (a − b)² = a² − 2ab + b² to find 62².
6. 6.Use a² − b² = (a + b)(a − b) to find 28² − 27².
7. 7.Use (a + b)² = a² + 2ab + b² to find 75².
8. 8.If a + b = 17 and ab = 72, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 29² − 3².
10. 10.Use (a − b)² = a² − 2ab + b² to find 27².
11. 11.If a + b = 14 and ab = 33, what is a² + b²?
12. 12.Use a² − b² = (a + b)(a − b) to find 73² − 15².
13. 13.Find the value of x² − y² when x = 3 and y = 2.
14. 14.Use a² − b² = (a + b)(a − b) to find 24² − 13².
15. 15.Use (a − b)² = a² − 2ab + b² to find 14².
16. 16.Find the value of x² + 2xy + y² when x = 7 and y = 5.
17. 17.Use (a + b)² = a² + 2ab + b² to find 49².
18. 18.Use a² − b² = (a + b)(a − b) to find 41² − 1².
19. 19.Use a² − b² = (a + b)(a − b) to find 37² − 7².
20. 20.Use (a − b)² = a² − 2ab + b² to find 91².
21. 21.If a − b = 1 and ab = 30, what is a² + b²?
22. 22.Use (a + b)(a − b) = a² − b² to find 52 × 48.
23. 23.Find the value of x² + 2xy + y² when x = 9 and y = 8.
24. 24.Use (a + b)(a − b) = a² − b² to find 55 × 45.
25. 25.Use (a − b)² = a² − 2ab + b² to find 52².
26. 26.Use a² − b² = (a + b)(a − b) to find 26² − 6².
27. 27.If a − b = 3 and ab = 4, what is a² + b²?
28. 28.If a − b = 4 and ab = 96, what is a² + b²?
29. 29.If a + b = 20 and ab = 99, what is a² + b²?
30. 30.Find the value of x² − 2xy + y² when x = 12 and y = 4.
31. 31.Use a² − b² = (a + b)(a − b) to find 41² − 5².
32. 32.Find the value of x² + 2xy + y² when x = 14 and y = 1.
33. 33.Use (a − b)² = a² − 2ab + b² to find 39².
34. 34.Use (a + b)² = a² + 2ab + b² to find 33².
35. 35.Use (a − b)² = a² − 2ab + b² to find 65².
36. 36.Use (a − b)² = a² − 2ab + b² to find 97².
37. 37.Find the value of x² − y² when x = 12 and y = 4.
38. 38.Use (a + b)(a − b) = a² − b² to find 65 × 55.
39. 39.Find the value of x² − y² when x = 6 and y = 5.
40. 40.Find the value of x² − y² when x = 7 and y = 5.

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