Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 363 · 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 55² − 32².
2. 2.Use a² − b² = (a + b)(a − b) to find 37² − 30².
3. 3.Use (a + b)(a − b) = a² − b² to find 96 × 84.
4. 4.Use (a + b)(a − b) = a² − b² to find 67 × 53.
5. 5.Use (a − b)² = a² − 2ab + b² to find 78².
6. 6.Use a² − b² = (a + b)(a − b) to find 62² − 2².
7. 7.Use (a + b)² = a² + 2ab + b² to find 36².
8. 8.Use (a − b)² = a² − 2ab + b² to find 89².
9. 9.If a + b = 18 and ab = 77, what is a² + b²?
10. 10.If a − b = 1 and ab = 6, what is a² + b²?
11. 11.Use (a + b)² = a² + 2ab + b² to find 85².
12. 12.Use (a − b)² = a² − 2ab + b² to find 45².
13. 13.Use (a + b)² = a² + 2ab + b² to find 91².
14. 14.Use (a − b)² = a² − 2ab + b² to find 46².
15. 15.Find the value of x² − y² when x = 4 and y = 3.
16. 16.Use a² − b² = (a + b)(a − b) to find 36² − 22².
17. 17.Use (a + b)(a − b) = a² − b² to find 23 × 17.
18. 18.Use a² − b² = (a + b)(a − b) to find 90² − 46².
19. 19.Use a² − b² = (a + b)(a − b) to find 91² − 36².
20. 20.Use a² − b² = (a + b)(a − b) to find 38² − 29².
21. 21.Use (a + b)(a − b) = a² − b² to find 32 × 28.
22. 22.Use (a + b)² = a² + 2ab + b² to find 86².
23. 23.Find the value of x² − y² when x = 12 and y = 3.
24. 24.Use (a − b)² = a² − 2ab + b² to find 54².
25. 25.Use (a − b)² = a² − 2ab + b² to find 76².
26. 26.Use (a − b)² = a² − 2ab + b² to find 37².
27. 27.If a − b = 6 and ab = 16, what is a² + b²?
28. 28.Find the value of x² − y² when x = 10 and y = 8.
29. 29.Find the value of x² − y² when x = 11 and y = 9.
30. 30.Find the value of x² − 2xy + y² when x = 5 and y = 3.
31. 31.Use (a − b)² = a² − 2ab + b² to find 52².
32. 32.Use a² − b² = (a + b)(a − b) to find 27² − 17².
33. 33.If a − b = 2 and ab = 80, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 44².
35. 35.Find the value of x² − y² when x = 7 and y = 6.
36. 36.Find the value of x² + 2xy + y² when x = 5 and y = 3.
37. 37.Use a² − b² = (a + b)(a − b) to find 28² − 2².
38. 38.Use (a − b)² = a² − 2ab + b² to find 87².
39. 39.If a + b = 11 and ab = 28, what is a² + b²?
40. 40.Use (a + b)(a − b) = a² − b² to find 31 × 29.

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