Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 852 · 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 91².
2. 2.Use a² − b² = (a + b)(a − b) to find 33² − 18².
3. 3.If a + b = 8 and ab = 15, what is a² + b²?
4. 4.If a + b = 10 and ab = 21, what is a² + b²?
5. 5.If a + b = 11 and ab = 28, what is a² + b²?
6. 6.Use (a + b)² = a² + 2ab + b² to find 45².
7. 7.Use (a + b)(a − b) = a² − b² to find 21 × 19.
8. 8.Use (a − b)² = a² − 2ab + b² to find 47².
9. 9.Use (a − b)² = a² − 2ab + b² to find 14².
10. 10.Use a² − b² = (a + b)(a − b) to find 72² − 13².
11. 11.Find the value of x² − y² when x = 9 and y = 6.
12. 12.Use (a + b)(a − b) = a² − b² to find 45 × 35.
13. 13.Use (a + b)² = a² + 2ab + b² to find 35².
14. 14.Use (a + b)(a − b) = a² − b² to find 92 × 88.
15. 15.Use a² − b² = (a + b)(a − b) to find 37² − 31².
16. 16.Find the value of x² + 2xy + y² when x = 3 and y = 1.
17. 17.Use (a + b)² = a² + 2ab + b² to find 34².
18. 18.Use a² − b² = (a + b)(a − b) to find 92² − 12².
19. 19.Find the value of x² − y² when x = 6 and y = 3.
20. 20.Use (a + b)(a − b) = a² − b² to find 53 × 47.
21. 21.Use (a − b)² = a² − 2ab + b² to find 23².
22. 22.Use (a + b)(a − b) = a² − b² to find 96 × 84.
23. 23.If a + b = 3 and ab = 2, what is a² + b²?
24. 24.Find the value of x² − y² when x = 3 and y = 2.
25. 25.If a + b = 13 and ab = 42, what is a² + b²?
26. 26.Use (a + b)² = a² + 2ab + b² to find 63².
27. 27.Use (a − b)² = a² − 2ab + b² to find 37².
28. 28.Use (a + b)² = a² + 2ab + b² to find 16².
29. 29.Use a² − b² = (a + b)(a − b) to find 87² − 2².
30. 30.Use (a − b)² = a² − 2ab + b² to find 34².
31. 31.Find the value of x² − y² when x = 5 and y = 4.
32. 32.Use (a − b)² = a² − 2ab + b² to find 54².
33. 33.Use (a − b)² = a² − 2ab + b² to find 35².
34. 34.Find the value of x² − 2xy + y² when x = 4 and y = 3.
35. 35.Use a² − b² = (a + b)(a − b) to find 26² − 12².
36. 36.Find the value of x² − y² when x = 7 and y = 6.
37. 37.Use (a + b)² = a² + 2ab + b² to find 42².
38. 38.If a + b = 14 and ab = 45, what is a² + b²?
39. 39.Use (a − b)² = a² − 2ab + b² to find 57².
40. 40.If a + b = 6 and ab = 5, what is a² + b²?

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