Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 160 · 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 = 12 and y = 4.
2. 2.Use (a + b)² = a² + 2ab + b² to find 58².
3. 3.If a − b = 6 and ab = 7, what is a² + b²?
4. 4.If a + b = 5 and ab = 4, what is a² + b²?
5. 5.Find the value of x² + 2xy + y² when x = 10 and y = 7.
6. 6.Use (a + b)(a − b) = a² − b² to find 23 × 17.
7. 7.Use (a + b)² = a² + 2ab + b² to find 21².
8. 8.Use (a + b)² = a² + 2ab + b² to find 79².
9. 9.Use a² − b² = (a + b)(a − b) to find 35² − 2².
10. 10.Find the value of x² + 2xy + y² when x = 4 and y = 3.
11. 11.Find the value of x² − y² when x = 8 and y = 2.
12. 12.Use (a + b)(a − b) = a² − b² to find 97 × 83.
13. 13.Use (a + b)² = a² + 2ab + b² to find 16².
14. 14.Use (a + b)² = a² + 2ab + b² to find 68².
15. 15.Use (a + b)² = a² + 2ab + b² to find 11².
16. 16.Use (a + b)² = a² + 2ab + b² to find 29².
17. 17.If a − b = 1 and ab = 6, what is a² + b²?
18. 18.If a + b = 9 and ab = 20, what is a² + b²?
19. 19.Use (a + b)(a − b) = a² − b² to find 34 × 26.
20. 20.Use a² − b² = (a + b)(a − b) to find 85² − 30².
21. 21.If a − b = 8 and ab = 48, what is a² + b²?
22. 22.Use a² − b² = (a + b)(a − b) to find 57² − 29².
23. 23.Use (a + b)² = a² + 2ab + b² to find 31².
24. 24.Use (a + b)² = a² + 2ab + b² to find 22².
25. 25.Find the value of x² − 2xy + y² when x = 6 and y = 2.
26. 26.Use (a − b)² = a² − 2ab + b² to find 91².
27. 27.If a − b = 2 and ab = 3, what is a² + b²?
28. 28.Use (a + b)(a − b) = a² − b² to find 35 × 25.
29. 29.Use (a − b)² = a² − 2ab + b² to find 61².
30. 30.Use (a + b)² = a² + 2ab + b² to find 102².
31. 31.Use a² − b² = (a + b)(a − b) to find 33² − 16².
32. 32.Use (a + b)² = a² + 2ab + b² to find 43².
33. 33.Use (a + b)(a − b) = a² − b² to find 37 × 23.
34. 34.Use a² − b² = (a + b)(a − b) to find 21² − 2².
35. 35.Use (a − b)² = a² − 2ab + b² to find 22².
36. 36.Find the value of x² + 2xy + y² when x = 11 and y = 7.
37. 37.Use (a − b)² = a² − 2ab + b² to find 19².
38. 38.Use (a − b)² = a² − 2ab + b² to find 69².
39. 39.Use a² − b² = (a + b)(a − b) to find 45² − 22².
40. 40.Use (a − b)² = a² − 2ab + b² to find 54².

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