Class 8 Maths Worksheet: Algebraic Identities

Maths worksheets lesson 61: Algebraic identities · Set 703 · 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 a² − b² = (a + b)(a − b) to find 51² − 14².
2. 2.Use (a − b)² = a² − 2ab + b² to find 62².
3. 3.Use (a + b)² = a² + 2ab + b² to find 77².
4. 4.Use a² − b² = (a + b)(a − b) to find 99² − 7².
5. 5.Use a² − b² = (a + b)(a − b) to find 83² − 21².
6. 6.Use (a + b)(a − b) = a² − b² to find 97 × 83.
7. 7.Use (a + b)² = a² + 2ab + b² to find 91².
8. 8.If a − b = 9 and ab = 36, what is a² + b²?
9. 9.Use a² − b² = (a + b)(a − b) to find 52² − 14².
10. 10.Use (a − b)² = a² − 2ab + b² to find 45².
11. 11.Use (a + b)² = a² + 2ab + b² to find 53².
12. 12.Use (a + b)² = a² + 2ab + b² to find 73².
13. 13.If a − b = 1 and ab = 56, what is a² + b²?
14. 14.If a − b = 5 and ab = 36, what is a² + b²?
15. 15.Find the value of x² − y² when x = 10 and y = 3.
16. 16.Use (a + b)(a − b) = a² − b² to find 77 × 63.
17. 17.Use (a + b)² = a² + 2ab + b² to find 68².
18. 18.If a − b = 2 and ab = 3, what is a² + b²?
19. 19.Use a² − b² = (a + b)(a − b) to find 44² − 20².
20. 20.If a − b = 3 and ab = 4, what is a² + b²?
21. 21.Use a² − b² = (a + b)(a − b) to find 54² − 21².
22. 22.Use (a + b)(a − b) = a² − b² to find 31 × 29.
23. 23.If a − b = 7 and ab = 8, what is a² + b²?
24. 24.Find the value of x² − 2xy + y² when x = 13 and y = 8.
25. 25.Use (a − b)² = a² − 2ab + b² to find 75².
26. 26.Use a² − b² = (a + b)(a − b) to find 91² − 12².
27. 27.Use (a − b)² = a² − 2ab + b² to find 13².
28. 28.Use (a − b)² = a² − 2ab + b² to find 57².
29. 29.Use (a + b)² = a² + 2ab + b² to find 37².
30. 30.If a + b = 15 and ab = 36, what is a² + b²?
31. 31.Find the value of x² − y² when x = 3 and y = 1.
32. 32.Use (a + b)² = a² + 2ab + b² to find 42².
33. 33.If a − b = 4 and ab = 60, what is a² + b²?
34. 34.Find the value of x² − y² when x = 9 and y = 8.
35. 35.If a + b = 4 and ab = 3, what is a² + b²?
36. 36.Use (a + b)² = a² + 2ab + b² to find 24².
37. 37.Use (a + b)² = a² + 2ab + b² to find 22².
38. 38.Use a² − b² = (a + b)(a − b) to find 30² − 25².
39. 39.Find the value of x² − y² when x = 7 and y = 1.
40. 40.If a − b = 1 and ab = 90, what is a² + b²?

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