Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 765 · 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 = 4 and y = 3.
2. 2.Use (a + b)(a − b) = a² − b² to find 23 × 17.
3. 3.Use (a + b)(a − b) = a² − b² to find 82 × 78.
4. 4.Use (a + b)² = a² + 2ab + b² to find 92².
5. 5.Use (a + b)(a − b) = a² − b² to find 62 × 58.
6. 6.Find the value of x² − 2xy + y² when x = 14 and y = 6.
7. 7.Use (a + b)² = a² + 2ab + b² to find 36².
8. 8.Use a² − b² = (a + b)(a − b) to find 35² − 6².
9. 9.Use a² − b² = (a + b)(a − b) to find 58² − 47².
10. 10.Find the value of x² − y² when x = 8 and y = 4.
11. 11.Use (a + b)(a − b) = a² − b² to find 71 × 69.
12. 12.Use (a + b)(a − b) = a² − b² to find 103 × 97.
13. 13.If a + b = 7 and ab = 6, what is a² + b²?
14. 14.Use a² − b² = (a + b)(a − b) to find 91² − 40².
15. 15.If a + b = 15 and ab = 44, what is a² + b²?
16. 16.Use (a − b)² = a² − 2ab + b² to find 37².
17. 17.Use a² − b² = (a + b)(a − b) to find 30² − 7².
18. 18.Find the value of x² + 2xy + y² when x = 11 and y = 5.
19. 19.If a − b = 2 and ab = 8, what is a² + b²?
20. 20.Use (a + b)(a − b) = a² − b² to find 86 × 74.
21. 21.Use (a − b)² = a² − 2ab + b² to find 28².
22. 22.Use (a − b)² = a² − 2ab + b² to find 89².
23. 23.Find the value of x² − y² when x = 3 and y = 1.
24. 24.Use (a + b)² = a² + 2ab + b² to find 61².
25. 25.Use (a − b)² = a² − 2ab + b² to find 44².
26. 26.Find the value of x² − 2xy + y² when x = 15 and y = 10.
27. 27.Use (a − b)² = a² − 2ab + b² to find 29².
28. 28.Use (a + b)² = a² + 2ab + b² to find 101².
29. 29.If a + b = 5 and ab = 4, what is a² + b²?
30. 30.Use (a − b)² = a² − 2ab + b² to find 76².
31. 31.Use a² − b² = (a + b)(a − b) to find 80² − 3².
32. 32.Use (a + b)(a − b) = a² − b² to find 89 × 71.
33. 33.If a + b = 16 and ab = 48, what is a² + b²?
34. 34.If a − b = 9 and ab = 10, what is a² + b²?
35. 35.Use (a + b)(a − b) = a² − b² to find 53 × 47.
36. 36.If a + b = 14 and ab = 45, what is a² + b²?
37. 37.If a + b = 7 and ab = 10, what is a² + b²?
38. 38.Use (a + b)² = a² + 2ab + b² to find 87².
39. 39.Use a² − b² = (a + b)(a − b) to find 84² − 13².
40. 40.Use (a + b)² = a² + 2ab + b² to find 37².

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