Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 324 · 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 − y² when x = 7 and y = 3.
2. 2.Find the value of x² + 2xy + y² when x = 12 and y = 11.
3. 3.Find the value of x² + 2xy + y² when x = 9 and y = 8.
4. 4.Use (a + b)(a − b) = a² − b² to find 53 × 47.
5. 5.If a + b = 7 and ab = 12, what is a² + b²?
6. 6.Find the value of x² − 2xy + y² when x = 5 and y = 2.
7. 7.Use (a − b)² = a² − 2ab + b² to find 19².
8. 8.Use (a − b)² = a² − 2ab + b² to find 23².
9. 9.Use (a + b)² = a² + 2ab + b² to find 57².
10. 10.If a + b = 11 and ab = 18, what is a² + b²?
11. 11.If a + b = 21 and ab = 110, what is a² + b²?
12. 12.Use (a + b)(a − b) = a² − b² to find 58 × 42.
13. 13.Use (a + b)(a − b) = a² − b² to find 83 × 77.
14. 14.Use (a + b)² = a² + 2ab + b² to find 59².
15. 15.If a + b = 11 and ab = 24, what is a² + b²?
16. 16.Use (a + b)² = a² + 2ab + b² to find 18².
17. 17.Use (a + b)² = a² + 2ab + b² to find 73².
18. 18.Use (a + b)(a − b) = a² − b² to find 47 × 33.
19. 19.If a + b = 4 and ab = 3, what is a² + b²?
20. 20.Find the value of x² + 2xy + y² when x = 4 and y = 1.
21. 21.Use a² − b² = (a + b)(a − b) to find 63² − 22².
22. 22.Use (a + b)² = a² + 2ab + b² to find 78².
23. 23.Use (a − b)² = a² − 2ab + b² to find 18².
24. 24.Use (a + b)² = a² + 2ab + b² to find 79².
25. 25.Use (a + b)² = a² + 2ab + b² to find 56².
26. 26.Find the value of x² + 2xy + y² when x = 10 and y = 3.
27. 27.Use (a − b)² = a² − 2ab + b² to find 24².
28. 28.Find the value of x² − y² when x = 9 and y = 2.
29. 29.If a + b = 5 and ab = 6, what is a² + b²?
30. 30.Use (a + b)(a − b) = a² − b² to find 34 × 26.
31. 31.Use a² − b² = (a + b)(a − b) to find 35² − 24².
32. 32.If a − b = 2 and ab = 63, what is a² + b²?
33. 33.If a + b = 8 and ab = 12, what is a² + b²?
34. 34.Use (a + b)(a − b) = a² − b² to find 82 × 78.
35. 35.Find the value of x² + 2xy + y² when x = 4 and y = 3.
36. 36.Use a² − b² = (a + b)(a − b) to find 72² − 53².
37. 37.Find the value of x² − 2xy + y² when x = 4 and y = 1.
38. 38.Find the value of x² + 2xy + y² when x = 11 and y = 7.
39. 39.Find the value of x² + 2xy + y² when x = 11 and y = 4.
40. 40.Use (a + b)(a − b) = a² − b² to find 46 × 34.

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