Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 926 · 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 (a + b)² = a² + 2ab + b² to find 103².
2. 2.Use (a − b)² = a² − 2ab + b² to find 62².
3. 3.Use a² − b² = (a + b)(a − b) to find 85² − 79².
4. 4.Find the value of x² − 2xy + y² when x = 11 and y = 2.
5. 5.Use (a − b)² = a² − 2ab + b² to find 22².
6. 6.Use (a − b)² = a² − 2ab + b² to find 36².
7. 7.Find the value of x² + 2xy + y² when x = 7 and y = 4.
8. 8.If a − b = 4 and ab = 5, what is a² + b²?
9. 9.Find the value of x² − y² when x = 14 and y = 3.
10. 10.Find the value of x² − y² when x = 13 and y = 6.
11. 11.Use a² − b² = (a + b)(a − b) to find 68² − 35².
12. 12.If a + b = 11 and ab = 28, what is a² + b²?
13. 13.Use (a + b)² = a² + 2ab + b² to find 97².
14. 14.Find the value of x² − y² when x = 3 and y = 2.
15. 15.Use (a + b)(a − b) = a² − b² to find 38 × 22.
16. 16.If a + b = 18 and ab = 80, what is a² + b²?
17. 17.Use (a − b)² = a² − 2ab + b² to find 76².
18. 18.Use (a + b)(a − b) = a² − b² to find 73 × 67.
19. 19.Use (a + b)(a − b) = a² − b² to find 63 × 57.
20. 20.Use (a + b)(a − b) = a² − b² to find 35 × 25.
21. 21.Use (a − b)² = a² − 2ab + b² to find 87².
22. 22.Find the value of x² − 2xy + y² when x = 13 and y = 10.
23. 23.Use (a + b)(a − b) = a² − b² to find 99 × 81.
24. 24.Use a² − b² = (a + b)(a − b) to find 57² − 32².
25. 25.Find the value of x² + 2xy + y² when x = 11 and y = 7.
26. 26.Use (a + b)(a − b) = a² − b² to find 55 × 45.
27. 27.Use a² − b² = (a + b)(a − b) to find 35² − 34².
28. 28.If a + b = 10 and ab = 21, what is a² + b²?
29. 29.If a + b = 6 and ab = 8, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 65 × 55.
31. 31.Find the value of x² − 2xy + y² when x = 5 and y = 1.
32. 32.Use a² − b² = (a + b)(a − b) to find 68² − 57².
33. 33.If a − b = 2 and ab = 3, what is a² + b²?
34. 34.Use (a − b)² = a² − 2ab + b² to find 37².
35. 35.Use a² − b² = (a + b)(a − b) to find 97² − 90².
36. 36.Find the value of x² + 2xy + y² when x = 4 and y = 3.
37. 37.Use a² − b² = (a + b)(a − b) to find 51² − 21².
38. 38.Use (a − b)² = a² − 2ab + b² to find 19².
39. 39.Find the value of x² − 2xy + y² when x = 6 and y = 3.
40. 40.Use (a + b)(a − b) = a² − b² to find 44 × 36.

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